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Physics 2121 Lab Manual

1. Material Index Material Index Vacuum 1 00000 Rock Salt 1 544 Water gas 1 000261 Sodium Chloride 1 544 Argon 1 000281 Quartz 1 544 Air at STP 1 0002926 Amethyst 1 544 Nitrogen liq 1 2053 Amber 1 546 Alcohol 1 329 Polystyrene 1 55 1 59 Ice 1 309 Emerald Synth flux 1 561 Water 100 C 1 31819 Emerald Synth hydro 1 568 Methanol 1 329 Flint glasses 1 57 1 75 Water 35 C Room temp 1 33157 Glass Flint Light 1 58038 Water 20 C 1 33335 Styrofoam 1 595 Teflon 1 35 Topaz Blue 1 610 Acetone 1 36 Turquoise 1 610 Ethanol 1 36 Mercury liquid 1 62 Ethyl Alcohol 1 36 Topaz 1 620 Sugar solution 30 1 38 Topaz Pink 1 620 Fluorite 1 433 Topaz Yellow 1 620 Aluminum 1 44 Topaz White 1 630 Opal 1 450 Glass Flint Medium 1 62725 Quartz Fused 1 45843 Carbon disulfide 1 63 Plastic 1 460 Asphalt 1 635 Turpentine 1 472 Glass Flint Heavy 1 65548 Glycerine 1 473 Glass Flint Dense 1 66 Onyx 1 486 Olivine 1 670 Glass Albite 1 4890 Methylene iodide 1 74 Sugar solution 80 1 49 Ruby 1 760 Ulexite 1 490 Sapphire 1 760 1 77 Plexiglas 1 50 Rare earth flint 1 7 1 84 Dolomite 1 503 Glass Flint Lanthanum 1 80 Gaylussite 1 517 Pyrite 1 810 Glass 1 51714 Lanthanum flint 1 82 1 98 Rubber Natural 1 5191 Glass Flint Heaviest 1 89 Crown glasses 1 52 1 62 Sulphur 1 960 Typical crown glass 1 52 Crystal 2 00 Nylon 1 53 Arsenic trisulfide glass 2 04 Thomsonite 1 530 Zirconia Cubic 2 170 Sodium chloride 1 54 Diamond 2 417
2. Results Complete Table 1 Linear V V Frequency Conclusion Please include a conclusion statement with your write up 74 Laboratory 9 Report Sheet RLC Circuits Experimenters Course Date Purpose The purpose of this activity is to study the currents and voltages We will measure the response of the voltage across a resistor V as a function of a voltage applied at different frequencies Introduction and Theory Schematic f adjustable frequency o 2nf V voltage I current Overall resistance V V mie aa _ 2 _ 2 x _ 1 Z ol 7 Z R X Xc where X L and T 75 The smallest Z occurs when X X Resonance condition L C L C R __ L 1 92mH 1 92 10 H C 1uF 1 10 F a Calculate f theoretically b Determine experimentally the value of f experimentally 2 T T lo or Vo Power or amplitude 2 1 2 V 1 1 P gt litude I R or gt Ln F l Ving avg z amp tu e rms or R rms v2 0 rms J2 1 1 Va V rms J2 E V ns Lym R rms Oscilloscope reads Vo AC meter reads J V rms rms 76 Q or Quality of circuit R small XL gt Xc R medium Current Amplitude R high fi Frequency f Equipment The following components can be used as is or substituted by PASCO s AC DC Electronics Laboratory System Oscilloscope Function Generator I
3. Theory The defining equation for the index of refraction between any two materials is Na Sin a ng sin p 83 where a is the bending angle with respect to the external medium is the bending angle with respect to the internal medium n is the index of refraction of the external medium and ng is the index of refraction of the internal medium Laser Beam Medium a Medium For the case where the medium a is air then na is nearly one and we can rearrange the above equation to solve for the index of refraction of the material as sina n where n n sin 2 p We will use a red laser beam as a source for the light ray a laser generates a coherent monochromatic light beam with which to find the index of refraction of a slab of transparent material This value for the index of refraction is valid only for photons that have the same wavelength as those from the laser Equipment Laser 1 Glass block 1 Protractor or circular optics table 1 Procedure 1 Use the materials listed and the above equation to determine the index of refraction of the glass block A good procedure is to lay the block flat on a piece of paper and shine the laser light through the edge at a sufficiently large angle Make a mark on the paper where the light enters and leaves the block Construct perpendicular lines to the face of the edge to be used for measuring the appropriate angles 84 2 What are the units
4. 2 Draw a good representation of the magnetic field lines produced by the solenoid shown on the back of this page The magnitude of the magnetic field along the axis of an N turn coil Helmholtz coil is LL NIR 3 2 x R where is the current R is the radius of the coil and x is axial distance from the coil s center 3 What is the magnitude of the magnetic field at the center of a 100 turn Helmholtz coil of radius 5 0 cm carrying an 0 5 A current 4 What is the magnitude of the magnetic field produced by that Helmholtz coil at a point on the solenoid s axis 3 0 m from its center Laboratory D Magnetic Fields Purpose The purpose of this experiment is to understand magnetic fields and how they behave through the mapping of the field lines and through investigations of electromagnetism An optional set of computer simulations is included near the end Introduction and Theory A magnetic field is a vector force field generated by a magnetic dipole that can exert a force on a moving electric charge or another magnetic dipole Field lines are used to graphically indicate the direction of the field and the density of the lines indicates the strength of the field These force fields can also be generated by electric currents of various sizes These currents can be macroscopic as is the case in electromagnets or microscopic as is true for permanent dipole or bar magnets In the microscopic case the magnetic
5. Error analysis It is up to your instructor whether some form of error analysis will be included in your lab assignments It is recommended for the University Physics Laboratories but not necessarily recommended for the General Physics Laboratories In the event the instructor includes some form of error analysis in the course work a brief discussion on error propagation follows In physics we often do experiments where we wish to calculate a value that has a functional dependence on some measurable quantities for example y f x z or Y f staat In some cases we wish to determine how close our experimental value is compared to the published result This is usually performed by finding the percent difference between the experimental value and the theoretical value The percent difference is given by exp erimental theoretical diff x 100 theoretical NOTE Technically the term percent difference refers to the difference between a measured or experimentally determined value and a theoretical or reference value Percent error is the difference between two measurements of the same value made by two different methods Errors in measurement can readily be obtained in the following ways 1 If only one measurement was taken use 2 the smallest scale division of the measuring device 2 If multiple measurements were taken e use standard deviation function on your calculator e or use the standard deviation for
6. Set up the circuit shown above for two resistors in series For a fixed setting for the power supply 3 Measure the current in the circuit and the voltage drops across each of the resistors and the ammeter 4 Measure the closed circuit voltage across the battery 5 Remove the wires from the battery and measure the total resistance Req of the circuit by placing the ohmmeter leads on these two wires This is often called the open circuit resistance Parallel Circuit 47 6 Set up the circuit shown above for two resistors in parallel For a fixed setting of the power supply 7 Measure the total current in the circuit and the current in each branch 8 Measure the voltage drop across each resistor and ammeter To avoid further complexity call R R2 the series combination of the resistor and ammeter in that branch 9 Measure the open circuit resistance Reg Extra Credit Circuit 10 Set up the circuit shown above for three resistors in series and parallel For a fixed setting of the power supply 11 Measure the total current in the circuit and the current in each branch 12 Measure the voltage drop across each resistor and ammeter 13 Measure the open circuit resistance Reg 48 Data Series Combination Parallel Combination Extra Credit Ohmmeter measurements incl ammeter incl ammeter R R R R R NA NA R 8 R Ra Voltage measureme
7. a to verify Boyle s law and b to determine the absolute zero point of temperature Equipment Boyle s law apparatus Absolute Zero Apparatus Thermometer Ice for ice water bath Dry ice bath Liquid Nitrogen IL Bunsen Burner Base and Support Rod Beaker 1 5 L Buret Clamp SSeS SS Se Procedure A Boyle s Law Note The Boyle s Law experiment can be performed while waiting for the absolute zero experiment to come to equilibrium during one of the steps below 1 Before recording P vs V data using the Boyle s law apparatus depress and hold the syringe at the 15 ml mark and observe what happens to the pressure reading Does the syringe leak In the Discussion section discuss this problem and what technique you employed to minimize the error introduced by the leakage 2 Take up to 10 pressure readings at different volumes using the Boyle s law apparatus 3 Plot P vs V B Finding Absolute Zero 1 Put about 800 mL of water in a 1 5 L beaker and put the beaker on the support stand and bring to boiling over the Bunsen burner 14 Place the thermometer near the bulb of the absolute zero apparatus on the lab table Let the temperature in C and gas pressure have come to equilibrium and record the temperature and pressure Carefully place the bulb of the absolute temperature apparatus in the boiling water When the water returns to boiling 100 C and the gas pressure achieves an equilibrium record
8. at this jack The output is independent of the AMPL and OFFSET controls 9 VCF IN Jack Voltage Controlled Frequency input Permits external sweep or frequency control Positive voltage decreases the output frequency 11 FINE Frequency Control Vernier adjustment of output frequency for ease of setting to a precise frequency 13 Frequency Counter Display Displays frequency of internally generated frequency 15 GATE LED Indicates when frequency counter display is updated When the 10 K through 1 M frequency switches are selected the LED will flash 10 times per second every 0 1 second When the 10 through K switches are selected the LED will flash once each second and when the 1 switch is selected the LED will light every 10 seconds As the LED turns off the display is updated 2 Range Selectors Selects frequency range Decade frequency type seven ranges from 1 Hz to 1 MHz Frequency can be adjusted from 0 2 to 2 times the range selected For example if the 100 K range is selected frequency can be adjusted see Frequency Control from 20 kHz to 200 kHz Numbers under pushbuttons indicate gate time see GATE LED 4 AMPL Control Controls amplitude of signal at OUTPUT jack When control is pulled out signal is attenuated 20 dB PULL 20 dB 6 TTL CMOS When control is pushed in a TTL signal is present at the TTL CMOS jack Level is fixed at 3 V p p and turning control has no effect When the control is pul
9. plot equipotential lines with a voltmeter to be used for constructing the electric field which lies perpendicular to the equipotential lines Having completed this lab you will be able to 1 Map equipotential lines from various shaped electrodes 2 Map the shape of electric field lines from equipotential lines Introduction amp Theory Electric fields are defined as electric force per unit charge This is the region where electric forces are exerted on charges Much like a topographic map where contour lines show constant elevations equipotential lines have identical potentials along them That is to say if we took any two arbitrary points along an equipotential line and calculated the differences in potential between the two points AV V Va we would get zero The electric field E is defined as the electric force F per unit charge qo E F qo Electric field is a vector and by convention points in the direction of the force on a positive charge The electric force on a charge q is F gE where E is the electric force per unit charge produced from a distribution of charges F qo E For a small displacement As of a charge q the work done by the electric field on the charge is AW FeAs gE As The charge s path can be built up by many such small displacements Note that the work performed by the electric force depends only on the starting and end points and not on the path taken This means that the electric force
10. types of magnets To map out the magnetic field of a bar magnet follow the guidelines listed below Set the magnet near the center of the sheet of graph paper Starting about lcm on one side of the magnet near the middle place the compass until the needle stabilizes do not drop the compasses Draw a point on the paper on either side of the points of the compass needle Move the compass up or down one compass diameter and repeat Follow the direction of the needle if it begins to turn make sure you turn with it Continue this process connecting the dots as you go along until you reach a pole of the magnet Repeat for the other end toward the other pole and also for the other side of the magnet at an equivalent distance 115 After having plotted the first pair of magnetic field lines repeat the above steps for lines that parallel the magnet about 3cm 5cm 7cm and 10 cm away from the magnet If the instructor chooses he may have you map the magnetic field that surrounds a different type of magnet If so repeat the above steps for that magnet on a separate sheet of paper 2 Solenoids and Wire Coils This next activity makes use of the wire coils in the following manner starting with the solenoid There are several questions in the procedure that you will need to write responses for in the Results section of your laboratory report Connect the solenoid coil without its core to a DC power supply
11. 1 Of the five wires which one has the smallest resistance 2 Which one of the wires carries the smallest current when they are connected to identical batteries 3 What is the resistance of wire B Show work 4 Wire B is connected to the terminals of a 1 5 V battery What magnitude current flows through the wire 33 Laboratory 4 Ohm s Law and Resistivity Adapted from Jerry Wilson Physics Laboratory Experiments 4 Ed pp 353 357 1994 Houghton Mifflin Company Purpose The purpose of this experiment is to investigate the resistivity of several different types of wires Introduction and Theory _ Electric current is defined as the rate at which electric charge flows through a surface _ AQ At The SI unit of current is the ampere 1 A 1 C s The direction of current flow is conventionally the direction of flow of positive charge This sign convection is standard although in most cases current is carried mainly by electrons Electrons are relatively free to move in solid conductors and having less mass electrons undergo a greater acceleration then protons in a given electric field Ohm s law states that the potential difference V across a substance is proportional to the current flowing through it V J The proportionality is the resistance R V IR The MKS unit for resistance is the ohm Q Thus R V I The resistance of an electrical conductor depends on several factors suc
12. Div control knob How many vertical divisions are there from peak to peak What is the peak to peak voltage Vpp Remember V ____ volts div X ____div ___ volts What is the setting on the sec div control knob How many horizontal divisions are there What is the period T of the signal T ___sec div X__ div ____ sec What is the frequency f of the signal in Hertz Draw the displayed signal on the graph below Be neat to scale and concise Write down the scale V div and Sec div settings on the graph The next part is to adjust the function generator to output another signal and repeat the measurements in Step 1 1 ON Soe a Generate a sine wave between 5 and 10 kHz with an amplitude setting of at least 6 vertical divisions Adjust the V div and sec div settings to maximize the display of the signal on the CRT Make sure you show the signal from peak to peak and at least one full cycle period of the signal What is the setting on the Volts div control knob How many vertical divisions from peak to peak What is the peak to peak voltage Vpp Vpp ____ volts div X____ div __ volts What is the settings on the sec div control knob 98 7 How many horizontal divisions are there 8 What is the frequency f of the signal Hz 9 Draw the displayed signal on the graph next page Write down the scale V div and Sec div settings on the graph 99 Appendix Ba THE OSCILLOSCOPE TENMA Mo
13. Reverse its polarity Again test the vertical deflection Now observe the effect of the variable calibration control 15 Set the DC GND AC switch to AC and repeat the test with the battery and explain what happens Hint refer to Appendix A Repeat 4 but use an AC voltage source e g the AC line source box With the TRIGGER MODE switch 35 at AUTO set the TRIGGER SOURCE select switch 31 to CH 1 Adjust the TRIGGER LEVEL control knob 34 if the wave display is not stationary Measure on the horizontal scale the time period of voltage oscillation Compare your result with T f for f 60 Hz The horizontal time scale is chosen by knob 26 TIME DIV Test what happens when 31 is not set as indicated EXPLAIN See Appendix A Reset all controls and replace the AC line source box with the sine wave output of the function generator Adjust knob 13 so that the sine wave voltage amplitude about fills the CRT and vary the frequency of the function generator Start at about 70 Hz and increase by about factors of three to about 700 000 Hz Calculate the frequency at each interval by measuring the time for a full cycle as you did in part 6 Compare this measured value with the value you read off the function generator Which set of values are more precise Plot these data as frequency against frequency including appropriate error bars Does a straight line of slope 1 pass through the data including 0 0 Disconnect the function ge
14. accepted values listed below in p ois a ee Conductor j board A la e NOTE For best results the voltmeter should make contact with the resistance wire R about 5 cm in from the terminals not at the terminals 37 Data Substance Resistivity p Q cm Aluminum 2 8 x 10 Brass 7x 10 Constantan 49 x 10 Copper 1 72 x 10 German Silver 18 Ni 33 x 10 Iron 10x 10 Manganin 44 x 10 Mercury 95 8 x 10 Nichrome 100 x 10 Nickel 7 8x 10 Silver 1 6x 10 Tin 11 5 x 10 Ohm s Law Wire __4 copper V Voltage I Current Slope of V vs J R Average V Average I Wire __5 constantan V Voltage I Current 38 Slope of V vs I R Average V Average Resistivity Wire Diameter D Length Voltage V Current I 1 copper 2 copper 3 copper 4 copper Ave Ave 5 constantan Ave Ave D l bV Data analysis Wire Peale Pknown error uncertainty A copper B copper C copper D copper E constantan Summary Attach a typed Conclusion and Discussion section addressing any questions your professor may ask 39 Pre Laboratory Exercise 5 Series and Parallel Resistors Name Course Date Three resistors are placed in
15. changing flux can induce currents in other coils One practical use for inductance is to detect the presence of cars at a stoplight An inductive loop is a coil of wire that winds a certain number of turns This coil is embedded in the road s surface and works by detecting a change of inductance This change comes about when a large steel object the car is placed within the inductor s magnetic field and that changes the inductance which is detected by a meter which then sends a command to the light to switch from red to green after a short interval of time When electric current first starts flowing in a coil the coil s tendency is to build up a magnetic field While the field is building the coil inhibits the flow of current Once the magnetic field is built up the current flows normally through the wire When the switch is opened and the circuit is broken the magnetic field around the coil maintains an electric current until the magnetic field collapses The inductor has a characteristic called capacity which is influenced by two factors e The number of coils e The material that the coils are wrapped around the core Putting iron in the core of an inductor gives it much more inductance than air or any other non magnetic core would There are devices that can measure the inductance of a coil and the standard unit of measure is the Henry Magnetic flux is defined as the product of the magnetic field and the area through which the
16. controls B Measurement of DC and AC voltages Note Bold italic numbers below are knobs indicated schematically and described in Appendix A Also note Connections will typically be made with co axial cables that are terminated by BNC connectors A coaxial cable consists of a central wire surrounded by a dielectric typically plastic which is itself surrounded by a braided copper shield The signal typically travels on the center wire and the copper shield is grounded The center post of the BNC connector is attached 95 to the central wire and the metal twist lock on the BNC connector is attached to the grounded shield These connections are schematically shown in figures in the next two labs Using Channel 1 CH 1 or X controls only 1 Set the DC GND AC Switch 17 on GND 2 Adjust the vertical position knob 19 so the horizontal trace is vertically centered on the screen Now you can measure voltages relative to this ground position 3 Set the DC GND AC switch to DC 4 5 6 7 8 Turn the variable VAR dark gray knob 15 voltage control fully clockwise The surrounding light gray knob VOLTS DIV 13 can be adjusted to change the vertical scale calibration in volts per centimeter above and below the zero central or ground position The calibration is correct only when the dark gray knob is fully clockwise Test this vertical deflection with a 1 5 volt battery connected to the CH1 INPUT 9
17. equal to the initial position and the value of the slope is equal to the velocity The slope which is a representation of the average velocity has been calculated as 1 02 m s The best fit data for this graph using a least squares algorithm is printed at the top of the graph Its value for the slope is slightly less than the calculated value but is the more accurate value To within two significant figures the values for the slopes are the same and only two significant figures were used in the slope calculation However it is important to keep the third significant figure for future calculations to decrease cumulative round off errors Note well the best fit straight line does not extrapolate through the point 0 0 and so either the initial position of the device is less than zero or there is some distortion near zero or else there is a systematic error Laboratory Report Format The finer details of the Laboratory Report Format may vary from instructor to instructor but each will use a format similar to that described below The student will hand in written or typed reports If you type the report but do not have access to a proper equation writer then it is better to leave blank spaces and fill in the equations by hand For example vx 2 is not the same as vx 2 nor is x2 an acceptable substitute for x Ambiguous equations are much worse than hand written equations Students are expected to use the following laboratory report for
18. field arises from electrons in atomic orbits The magnetic field B is defined in terms of a force exerted on a moving test charge as exhibited by the Lorenz Force Law F qE qv xB The direction of the electric force is in the direction of the electric field if the charge on the test charge q is positive but the direction of the magnetic field is given by the right hand rule The magnetic field has units of Tesla and Gauss where 1 Tesla 10 000 Gauss The magnetic field due to a wire segment As is given by the Biot Savart Law 4 AB Asxr 47 with u 4r x 10 Tm A For complete circuits such as a circular loop of wire with a loop radius of R and N turns u NIR B 2 24372 U x R Y From the right hand rule with the fingers curled in the direction of electric current flow in the loop the thumb points in the direction that the magnetic field points along the axis of the current loop Current loops act like magnetic dipoles with a dipole moment of u IA with A being the area of the loop Coils of wire only produce magnetic fields when carrying electric current The magnetic field of such a setup drops as E at large R R 2 o 3 X At large x the magnetic field equation becomes At a distance the magnetic field from the loop is equivalent to that of a small permanent magnet 114 Note This lab has several variations which are included below The standard report sheet with its procedure is also
19. for the resonant angular frequency compare to the theoretical value for the resonant angular frequency 2 Is the plot of impedance current versus frequency symmetrical about the resonant frequency Explain At resonance the reactances of the inductor and the capacitor cancel each other out so that the impedance Z is equal to just the resistance R Calculate the resistance of the circuit by using the amplitude of the current at resonance in the equation R V I Is the resistance equal to that used in the circuit Why or why not Optional Electronic Workbench MultiSim Extension Purpose The purpose of this activity is study currents and voltages in RLC circuits We will measure the response of the voltage across a resistor Vr as a function of a voltage applied at different frequencies using Multisim Equipment Multisim software 72 Procedure Open the Multisim program Click on PLACE then click on COMPONENT Click on the drop down bar below GROUP and select BASIC Select RESISTOR and under COMPONENT select the value resistor then click ok Select CAPACITOR select the value then click ok Select INDUCTOR select the value then click ok Click on the drop down bar below GROUP select SOURCES then POWER_SOURCES then GROUND then click on ok Go to the same drop down bar select INDICATORS then select AMMETER the select AMMETER_H then click ok Then close the SELECT A COMPONENT tab Go to the right side of the program Run t
20. gases as the forces between the molecules overcome kinetic energy The gas becomes a liquid At still lower temperatures and higher pressures the liquid is forced into a rigid structure we call a solid For the ideal gas this gas would continue to have a constant pressure volume relationship For the ideal gas as the temperature decreases the volume and the pressure of the gas also decrease with the pressure and volume maintaining a constant relationship Theoretically one can use a graph of pressure versus temperature to estimate the value of Absolute Zero by finding the temperature that the pressure reaches zero Safety Reminder You may be working with liquid nitrogen and or dry ice in this lab either of which can produce severe frostbite on contact Be extremely careful and use gloves and eye protection when dipping the absolute zero apparatus bulb in the liquid nitrogen dewar One group at a time will be permitted to do this and it is strongly recommended that this be the last element that the bulb is exposed to that is have the other three or four pressure temperature measurements room temperature hot water ice water and dry ice if available measurements The temperature of the liquid nitrogen is given below DON T insert the thermometer in the Dewar 13 Laboratory 1 Report Sheet Finding Absolute Zero Experimenters Course Date Objective The objective of this experiment is
21. included The professor may decide to do one or the other or a combination of both Equipment Bar magnet 1 Neodynium or Rare Earth Magnet 1 Horseshoe magnet several Small compass 1 Solenoid with iron core 1 800 turn coil 1 DC Power supply 1 Ammeter amp Voltmeter or multimeter 1 each Connecting wires 4 Graph paper can use the same as was used in Several the Electric Field Mapping experiment sheets PC with Internet connection and Data Studio 1 Magnetic Field Sensor 1 Procedure Note this experiment is a collection of demonstration activities that explore the permanent magnet as well as the electromagnet The instructor may choose one or more of the suggested activities or perform one of his own choosing to demonstrate how magnetic fields work Included below are several activities which consist of both online and live hands on exercises In addition there are several demonstrations e g jumping ring magnet through a Helmholz coil hooked to a galvanometer Lenz s law etc that can be performed to illustrate concepts covered in this experiment 1 Permanent Magnet The first activity involves mapping the magnetic field in a manner similar to what we did earlier in the semester with the electric field In this case it is considerably simpler We will use small compasses magneto probes to trace out the magnetic field at various places to put together a picture of the magnetic field We will do this for several different
22. m s 1 4 s 480 396m Therefore the canyon wall is 480 396 meters away Bats use sound waves to hunt and navigate Bats produce and send short bursts of ultrasonic waves which hit the objects and reflect back They detect the time delay between sending and receiving waves and approximate the distance of the objects Automatic focus cameras use ultrasonic sound waves to determine the distance of the objects The camera sends short bursts of ultrasonic waves which hit the objects and reflect back A sensor detects the time it takes for the waves to return and then determines the distance of the object from the camera Air columns in pipes or tubes of fixed lengths have particular resonant frequencies An example is an organ pipe of length L with one end closed the air in the column when driven at particular frequencies vibrates in resonance The interference of the waves traveling down the tube and the reflected waves traveling up the tube produces longitudinal standing waves which have a node at the closed end of the tube and an antinode at the open end Sound travels through air at the speed of sound Officially the speed of sound is 331 3 meters per second 1 087 feet per second in dry air at 0 Celsius 32 Fahrenheit At a temperature like 28 C 82 F the speed is 346 meters per second The speed of sound changes depending on the temperature and the humidity but if you want a round number then something like 350 meters per second
23. potential This lab will show you how to measure and plot equipotential lines with a voltmeter to be used for constructing the electric field which lies perpendicular to the equipotential lines Having completed this lab you will be able to 1 Map equipotential lines from various shaped electrodes 2 Map the shape of electric field lines from equipotential lines Cal Power Supply Equipment Graph paper several sheets Conductive paper with electrode configuration 1 to 2 Push pins at least 6 Clip leads 1 pair Power supply 1 Multimeter or galvanometer 29 Procedure PR ANS Use the DC voltage setting on your multimeter to set your power supply to 6 or 9 volts DC Turn off power supply keeping the knob to the correct voltage setting Connect the assembly as shown in the figure above Turn on the power supply Using one end of your multimeter select a point between the two electrodes noting its x and y coordinate Use the other end to probe for the points where the voltage on the mulitmeter says zero this corresponds to AV 0 Make a table or just plot these points Move the reference end of your multimeter to another reference point and repeat step 5 until you have sufficient equipotential lines to draw the electric field with sufficient accuracy Draw lines which are perpendicular to all equipotentials to plot your electric field lines Repeat steps 2 6 for a different electrodes configuration Questio
24. power supply provides the various potential differences and currents for complete operation of the instrument The individual controls for the above circuits are identified in Fig 1 of Appendix A The corresponding list of controls and descriptions of their function are given in Appendix A as well Study this list and try to understand the function of as many of the controls as you can before going to the lab In lab you will experimentally study the functions of most of them Equipment Oscilloscope Function Generator DC Power Supply 60 Hz AC Power Source Coaxial Cables Ww eS eS Procedure A Familiarizing Yourself with the Oscilloscope To prepare the oscilloscope for operation follow the instructions for How to Produce the Bright Line in Appendix A These procedures will avoid damage to the various oscilloscope circuits at turn on At the conclusion of these procedures you will have observed the horizontal line called a trace Be sure the trace is not too bright or the electron beam might burn the phosphor on the screen e Now you should analyze and become familiar with the operation and functions of as many of the various controls as you can Design and perform simple tests for the controls Since most of these are fairly obvious you need not record them in your report unless something unusual happens If it does of course you should seek out the reason Performing Part B will help you become acquainted with various
25. resonance occurs is equal to a half wavelength for example DDAA SA Ss ae and 2 z ZzS Se for the next resonance When an antinode is at the open end of the tube a loud resonance tone is heard Hence lowering the water level in the tube and listening for successive resonances can determine the tube lengths for antinodes to be at the open end of the tube If the frequency f of the driving tuning fork is known and the wavelength is determined by measuring the difference in tube length between successive antinodes AL 2 or A 2AL the speed of sound in air v can be determined from Vs AF The speed of sound which is temperature dependent is given to a good approximation over the normal temperature range by v 331 5 0 67 m s with T the air temperature in degrees Celsius 19 Experimenters Course Laboratory 2 Report Sheet Speed of Sound in Air Date Objective The purpose of this experiment is to use resonance to measure the speed of sound in air Equipment Resonance tube apparatus Tuning Forks 500 1000 Hz stamped Rubber mallet or Block Meter stick Thermometer m We Procedure 1 Raise the water level to near the top of the tube by raising the reservoir can by depressing the can clamp and sliding it on the support rod With the water level near the top of the tube there should be little water in the can if this is not the case remove some water
26. return rapidly to its zero position If the time taken for one timing sweep is equal to the period of the voltage applied to the y plates the pattern will consist of one cycle of the y voltage If the sweep frequency is equal to f n the image will show n waves of the y voltage The required horizontal movement of the fluorescent spot can be produced by means of an x voltage that periodically increases uniformly with time and falls to zero instantaneously upon reaching a given value The wave form of such a linear sweep voltage is shown in Fig 2 Because of its shape this signal is called a sawtooth voltage PEE time lt lt voltage Figure 2 b The horizontal and vertical signal amplifiers The oscilloscope amplifiers serve two purposes 1 Providing sufficient voltage to give any desired deflection of the electron beam 2 Making possible the variation of the deflection voltages without drawing appreciable current from the source under observation or from the sweep generator 94 c The z axis modulation controls the intensity and focus of the electron beam d and e The synchronization circuit ties the sweep of the horizontal time base in with the vertical signal so that any harmonic signal can be displayed as a stationary pattern The horizontal sweep is begun by a signal or condition called the trigger A variety of triggers are available as well as a variety of display selections following the trigger f The
27. television signal Both TV V and TV H synchronize only when the synchronizing signal is negative 36 Z AXIS Input Input terminal for external intensity modulation signal 37 CAL 2V p p This terminal delivers the calibration voltage of 2 V p p Khz positive square wave 38 GND Terminal Ground terminal of oscilloscope mainframe 39 CH2 INV When this button is pressed the CH2 input signal is inverted and in the ADD mode the CH2 signal is also inverted 40 TRIG ALT If you set VERT MODE 21 to DUAL or ADD press CH1 or CH2 on the TRIGGER SOURCE switch 31 then press the TRIG ALT button the internal triggering source signal will display alternately from CH1 and CH2 41 SLOPE Triggering slope button Triggering occurs when the trigger signal crosses the trigger level by positive going course Triggering occurs when the trigger signal crosses the trigger signal by negative going course The TENMA Model 72 6805 Oscilloscope also provides the basic features of a Function Generator to satisfy general demand with simple and intuitional operation by adjusting the control knobs directly from the front panel for output waveform amplitude frequency and range All the function generator control knobs are located in the front panel with the same color 103 42 GENERATOR OUTPUT This is the main output terminal of the function generator with 50 ohms impedance 43 FREQUENCY RANGE DI
28. the pressure Place the bulb in the ice ice water bath Let the gas come to equilibrium with the ice water bath 0 C and record the pressure Very carefully surround the bulb of the absolute temperature apparatus with dry ice frozen CO2 Let the gas come into equilibrium with the dry ice 78 5 C and record the pressure Reaching equilibrium with the dry ice might take a while Very carefully place the bulb of the absolute temperature apparatus into the liquid nitrogen Let the gas come into equilibrium with the liquid nitrogen 196 C and record the pressure Plot pressure versus temperature in C Determine absolute zero from the y intercept of the T vs P curve with the T axis where P 0 Alternatively plot P vs 7 and that absolute zero intercept is the x intercept Data A Boyle s law 15 B Finding Absolute Zero P T CC 100 78 5 196 Data Analysis P vs V plot attached Intercept from plot Absolute zero CC Summary Attach a typed Conclusion section and a Discussion section 16 Pre Laboratory Exercise 2 Speed of Sound in Air Name Course Date An organ pipe is 2 0 m long Assume the pipe is cylindrical with one closed and one open end Show your calculations to obtain the answers below 1 What is the longest wavelength for a standing sound wave possibl
29. the best fit straight line do not start from a data point 10 If you use a computer graphing package ensure that you use it correctly Be wary of the cheap graphics packages that will graph out the x values as equally spaced categories Do not just join the points together you require a best fit straight line Ensure that there are enough grid lines so that a reasonable slope calculation can be performed Better still use a graphics package which does both the best fit straight line and the slope and intercept calculations for you The above graph is an example as to how you are to plot acquired data Note that the graph has the following attributes 1 Each axis has an informative title that contains units of measurement 2 There is a graph title 3 The axes are computed such that the data nearly covers the complete graph 4 There is a best fit straight line that most nearly goes through all of the data points 5 The graph is clearly linear because the data looks straight and is a good linear fit because all of the data points are near the best fit straight line 6 Since the data is linear it can be parameterized with the following equation X Xo vt 7 This equation is similar to the standard equation of a straight line 10 y a bx where a is the y intercept and b is the slope Compare the above two equations and note that the coefficients are equal that is a Xo b v The value of the y intercept is
30. turn the current on to 0 5 amp and record the mass value in the Force column of Table 1 1 Increase the current in 0 5 amp increments to a maximum of 5 0 amp each time recording the new Force value Data Processing Plot a graph of Force vertical axis versus Current horizontal axis 107 Analysis What is the nature of the relationship between these two variables What does this tell us about how changes in the current will affect the force acting on a wire that is inside a magnetic field Table 1 1 Data Current Mass Force Current Mass Force amps gram gram amps gram gram 0 0 3 0 0 5 39 1 0 4 0 15 4 5 2 0 5 0 2 5 Please attach a typed Conclusions Discussion section addressing any questions asked by your instructor do the same for each of the four magnetic force experiments 108 Experiment 2 Force versus Length of Wire Procedure Set up the apparatus as in Figure 2 1 Determine the length of the conductive foil on the Current Loop Current Loop Record this value under Length in Table 2 1 Main Unit Magnet Assembly If you are using a quadruple beam balance With no current flowing determine the mass of the Magnet Assembly Record this value on the line at the top of Table 2 1 1 1 gram Balance Set the current to 2 0 amps Determine the new Figure 2 1 Equipment Set
31. typed Summary Include the following 1 What did you find for the strength and orientation of Earth s magnetic field 2 How did your measurements compare to your theoretical expectations both for the field lines of a bar magnet and for the quantitative measurements of the magnetic field strength along the axis of the Helmholtz coil 2a Is the dependence of the magnetic field strength of Helmholtz coil with distance along the axis as expected 2b Does the field fall off as x with large distance as expected At what distance does this behavior begin 3 Discuss factors that could have influenced your quantitative measurements and what you did to minimize them 121
32. wire and a magnetic field Is it reasonable to assume that the strength of the magnetic field is directly proportional to the number of magnets What would happen if one of the magnets were put into the assembly backwards with its north pole next to the other magnets south poles If there is time try it Table 3 1 Data Mass Mass Numberof 0 I 0 gram Force gram Numberof I 0 1 0 Force Magnets gram Magnets gram gram gram 1 4 2 5 3 6 110 Experiment 4 Force versus Angle Procedure 1 Set up the apparatus as shown in Figure 4 1 If you are using a quadruple beam balance 2 Determine the mass of the Magnet Assembly with no current flowing Record this value in Table 4 1 Pa on the appropriate line SF 8608 Accessory Unit 3 Set the angle to 0 with the direction of the coil of wire approximately parallel to the magnetic field Set the current to 1 0 amp Determine the new mass of the Magnet Assembly Record this 0 01 gram Balance value under Mass in Table 4 1 Figure 4 1 Equipment Setup 4 Subtract the mass measured with no current flowing from the mass measured with current flowing Record the difference as the Force 5 Increase the angle in 5 increments up to 90 and then in 5 increments to 90 At each angle repeat the mass force measurement If you are using an electronic balance 2
33. L MODE DUAL trace operation When the ALT CHOP switch is released in the DUAL trace mode the input signals at CH1 and CH2 are alternately displayed normally used at faster sweep speeds When this switch is depressed in the DUAL trace mode the CH1 and CH2 inputs are chopped and displayed simultaneously normally used at slower sweep speeds 24 25 DC BAL Adjustment Controls The knobs are used for adjusting the attenuator balance See oscilloscope manual p 20 DC BAL adjustments for details 26 TIME DIV Select Switch Provides sweep time ranges from 0 2 uS div to 0 5 S div with 20 steps totally X Y In this setting the instrument is used as an X Y oscilloscope where the X horizontal signal is the input to CH1 and the Y vertical signal is the input to CH2 27 SWP VAR The sweep time of the TIME DIV can be varied continuously when this knob is not at the CAL position Counterclockwise rotation to the full delays the sweep by 2 5 times or more For normal operation rotate the knob to the CAL position and the sweep time will be calibrated to the preset value of the TIME DIV switch 29 HORIZONTAL POSITION CONTROL This knob is used to adjust the horizontal position of the trace or spot The trace is moved toward the right with clockwise rotation and toward the left with counterclockwise rotation 30 x10 MAG Magnify by 10 by pressing this button 31 TRIGGER SOURCE Select Switch Selects the internal triggerin
34. Physics 2121 Laboratory Manual Edited by Brian Cudnik and Gary Erickson Fall 2014 Table of Contents The following is a list of experiments prepared for Physics 2121 General Physics Laboratory IL These experiments are performed in room 301 of the E E O Banion New Science Building Accompanying the experiments are suggested pre lab activities that provide an orientation to each lab these are provided before the main write up The purpose of the pre lab is to get students to think ahead to the subsequent experiment so as to arrive better prepared on the day of the experiment A set of 10 experiments is used in the standard list of experiments but the individual instructor may switch one or two of them for another on the list or for exercises not included in this manual Instructor s Choice or may add one or more to the list Several of these labs involve use of PASCO computer interface equipment which works with the Dell computers in the lab In general the computerized version of a particular lab when applicable is presented alongside the traditional version giving the instructor a choice between the two for that particular lab A tutorial for using the computers and the computer interfaced equipment is located in a separate manual kept in room 305 Introduction to this document and the labs sisi icovcadnnss dotubs iadanspativeleatduas qalvbilaciaatecpeatwbtherdaanioae 3 Laboratory Safety Inform att Omics cis
35. Place the magnet assembly on the pan of the balance With no current flowing press the TARE button bringing the reading to 0 00 grams 3 Set the angle to 0 with the direction of the coil of wire approximately parallel to the magnetic field Set the current to 1 0 amp Record the mass value in the Force column of Table 4 1 4 Increase the angle in 5 increments up to 90 and then in 5 increments to 90 At each angle repeat the mass force measurement Data Processing Plot a graph of Force vertical axis versus Angle horizontal axis Analysis ee the relationship between these two variables How do changes in the angle between the current and the magnetic field affect the force acting between them What angle produces the greatest force What angle produces the least force Mass with I 0 Table 4 1 Data Angle Mass Force Angle Mass Force 0 Angle Mass Force Angle Mass Force 0 gram gram gram gram 0 gram gram 0 gram gram 0 50 0 50 5 55 5 55 10 60 10 60 15 65 15 65 20 70 20 70 25 75 25 75 30 80 30 80 35 85 35 85 40 90 40 90 45 45 111 APPENDIX D Magnetic Fields Laboratory Package Pre Laboratory Exercise D Magnetic Fields Name Course Date 1 Draw a good representation of the magnetic field lines produced by the bar magnet shown on the back of this page
36. SPLAY The selected frequency range is lighted up on this display panel 44 FREQUENCY KNOB This knob is used to adjust the frequency Rotate the knob clockwise to get higher frequency and rotate counterclockwise to get lower frequency 45 AMPLITUDE DC OFFSET Adjustment Knob The outer knob is used to adjust the amplitude of the wave Rotate clockwise to increase the amplitude and rotate counterclockwise to decrease the amplitude The inner knob is for DC Level adjustment and works only when the knob is pulled up Pull up the knob and rotate clockwise to get positive DC Level and reverse the rotation of the knob to get negative DC Level 46 FREQ RANGE Switch The frequency range can be selected by pressing this button following 1M 100k 10k 1k 100 10 and sequence 47 WAVEFORM SELECTOR Pushing this button will change the waveform following a Sine wave Triangle wave and Square wave sequence 48 OUTPUT WAVEFORM DISPLAY The current output waveform is lighted up on this display panel 104 Appendix Bb The Function Generator Controls and Indicators 1 PWR Switch Turns power on and off 3 Function Selectors Selects square triangle or sine waveform at OUTPUT jack 5 OUTPUT Jack Waveform selected by FUNCTION switches as well as the superimposed DC OFFSET voltage is available at this jack 7 TTL CMOS Jack Square wave selected by TTL CMOS control either TTL or CMOS is available
37. Turn on the power and adjust the potential to 10V you may wish to verify this setting with the voltmeter Bring the core into the opening of the solenoid about 34 the way inside Turn on and off the power supply and observe how this affects the core does it tug on the core as you switch on and off Does the coil attract the core in a certain direction or is one end of the core repelled Does the core have permanent north and south poles We will repeat part of the above procedure with the 800 turn coil but use the magnetic field sensor attached to the Science Workshop interface box and with DataStudio running Place the sensor inside and outside at various distances and perform the following tasks Connect the 800 turn coil to a DC power supply Turn on the power and adjust the potential to 10V you may wish to verify this setting with the voltmeter Measure the current Z with the ammeter and record it in the Results section data table Measure the R or radius of the coil loops e Calculate the magnetic field for a point at the center of the cavity of the coil es NIR loop using the equation B TE x R rap of the coil near the middle of 2R 3R 5R and 1OR UNIR 2x3 Repeat at distances from the side At what point would you use Take measurements of B at the same locations for which you did calculations How do the calculated and measured values compare to each other To better evaluate t
38. a circuit as shown The potential difference between points A and B is 30 V 60 Q 1 What is the equivalent resistance between points A and B 2 Complete the following table for the potential difference and current across each of the resistors R Q AV V I A 10 30 60 40 Laboratory 5 Series and Parallel Resistors Purpose The purpose of this lab is to learn how currents flow through simple linear series and parallel circuits Introduction and Theory Kirchoff s rules state the conservation of energy and charge in an electrical circuit and can be used to determine the distribution of current and voltage within an electrical circuit Kirchoff s loop rule expresses conservation of energy Loop rule The sum of the potential drops around any closed loop within a circuit is zero Simply put start from any part of a circuit go around a closed loop returning to the starting point and the potential must return to its starting value Kirchoff s junction rule expresses conservation of charge Junction rule The total current entering a junction must equal the total current leaving a junction A junction is an intersection of conductors wires If the current into a junction were different than the current leaving that junction then charge would accumulate at the junction This would result in an electric field along the wires directed toward or away from t
39. al exponential fit to obtain the time constant Print the fitted data noting the values used for the resistance and capacitance on the plot 57 13 Change the value of the resistance on the resistance box by a factor of 2 to 10 and repeat the experimental steps 7 12 Data and Data Analysis Experiment 1 V R C Theoretical t RC Experimental t charging Experimental t discharging Plots attached Experiment 2 Vo i R i C Theoretical t RC Experimental t charging Experimental t discharging Plots attached Conclusion Attach a typed Conclusion and Discussion section Questions For questions 1 and 2 below assume an RC circuit as above with V 10 V C 100 uF and R 10 kQ Show your work 1 Assuming the capacitor is initially uncharged what is the value of the voltage across the capacitor after 5 time constants 2 With V 1 V e V e it mathematically takes an infinite time for the capacitor in an RC circuit to discharge completely Practically how many time constants does it take for the capacitor to discharge to less than 1 of its initial voltage 3 What is the time constant of the circuit shown above 58 Pre Laboratory Exercise 7 Magnetic Force Name Course Date 1 An electron traveling horizontally enters a region where a uniform magnetic field is directed into the plane of the pa
40. ance occurs Refraction is the bending of light as it passes from one substance to another As light passes from a less dense to a more dense material it bends towards the perpendicular to the plane of the surface of the material Conversely light entering a less dense material will bend away from the perpendicular to the plane of the surface The amount of bending which occurs depends both on the wavelength of the light and the type of material through which the light is propagating A property of the material related to the amount of refractive bending is called the index of refraction of the material The index of refraction of a material is usually quoted with respect to vacuum where the vacuum is defined to have an index of refraction of one The index of refraction of air is almost that of a vacuum so light traveling in air can be considered to be in a vacuum This is a good approximation to an accuracy of three significant figures On the next page is a table of the index of refraction for a number of everyday items This list is composed from lists that appear on several websites such as_http hyperphysics phy astr gsu edu hbase tables indrf html and the interactive website http interactagram com physics optics refraction which provides a fairly detailed description of the phenomenon of refraction 82 Index of Refraction of Selected Materials
41. and 1 200 feet per second are 18 reasonable numbers to use So sound travels 1 kilometer in roughly 3 seconds and 1 mile in roughly 5 seconds The resonance frequencies of a pipe or tube depend on its length L Only a certain number of wavelengths can fit into the tube length with the node antinode requirements needed to produce resonance Resonance occurs when the length of the tube is nearly equal to an odd number of quarter wavelengths i e L 4 L 3A 4 L 51 4 or generally L n 4 with n 1 3 5 and 4L n Incorporating the frequency f and the speed v through the general relationship Af v or f v A we have nv T n 1 3 5 Hence an air column tube of length L has particular resonance frequencies and will be in resonance with the corresponding odd harmonic driving frequencies As can be seen in this equation the three experimental parameters involved in the resonance conditions of an air column are f v and L To study resonance in this experiment the length L of an air column will be varied for a given driving frequency instead of varying f for a fixed L as in the case of the closed organ pipe described above Raising and lowering the water level in a tube will vary the length of an air column As the length of the air column is increased more wavelength segments will fit into the tube The difference in the tube air column lengths when successive anti nodes are at the open end of the tube and
42. and the fact that the potential drop across each branch must be the same as the applied voltage Thus resistors in parallel are the same as the equivalent resistance 1 1 arallel a 2 parallel eq Schematic for a Parallel Circuit Vo applied voltage A ammeter V voltmeter R resistor one R resistor two The equivalent resistance of more complicated combinations of resistors can be determine by determining the equivalent resistance of series and parallel portions of a circuit then determining the equivalent resistance of those combinations 43 The following circuit can be examined for extra credit The regular procedure for this lab follows In addition the laboratory computers in NSCI 301 are equipped with the Electronic Workbench MultiSim utilities that are useful for supplementing the electronics based lab exercises with quality simulation Documentation about MultiSim and Electronics Workbench are available separately Optional Electronic Workbench MultiSim Extension Purpose or objective To validate Ohm s Law Equipment Multisim software and PC Procedure Series resistors Open the Multisim program Click on place source this symbol a which is in the upper left corner of the program Select POWER_SOURCES from the left column then DC_SOURCES from the right column and then click ok Go to anywhere on the page and left click Then select GROUND and click ok Place the GROUND
43. ane in direct proportion to the instantaneous voltage applied between the deflecting plates This pair of plates provides the y axis or vertical movement of the spot on the screen A pair of vertical plates provides the x axis or horizontal movement of the spot on the screen The screen of a cathode ray tube consists of a thin layer of a phosphor which is a material that luminesces as the result of bombardment by rapidly moving electrons The bombardment gives rise to both fluorescence and emission of light after bombardment The phosphor is applied to the inside of the end of the tube by spraying dusting or precipitation from a liquid Slow decay of phosphorescence makes possible the visual observation of non repeating transients and prevents flicker in the visual observation of periodic voltages of low frequency However if it is too slow it causes blurring whenever an image on the screen changes form The main circuits of an oscilloscope and their functions are described below in a through f Fig 1 of Appendix A to this experiment shows the control areas for these circuits for the Tenma 72 6805 oscilloscope similarly identified as a through f a The time base generator In order that the image plotted on the scope screen shall show the unknown y axis voltage as a function of time it is necessary that the spot shall periodically sweep across the screen horizontally along x axis with uniform velocity up to a certain point and then
44. anywhere below the POWER_SOURCE Go to the drop down menu that has sources click it and then select basic In the right column select the value resistor necessary and then click ok Click ok again to select another resistor until you get the required number of resistors Then click close to go to the circuit Connect the circuit by going to the tip of each component left click and then stretch the wire to the tip of the other component then left click to attach the wire to the other component Repeat this until the circuit is complete See figure 1 below 44 Figure 1 Resistors in series Now we want to confirm Ohm s Law by measuring the voltage drop across the resistors Let s measure the voltage drop across resistor R2 and the current between resistors R2 and R3 Click on place indicator this symbol E which is along the same row as the place sources symbol Click on VOLTMETER in the left column and click on VOLTMETER_H in the right column then click ok Then click on AMMETER in the left column and click on AMMETER_H in the right column click ok Then click close Connect wires from the VOLTMETER to the wire and from the AMMETER to the wire Click on the wire below the AMMETER and click delete The circuit should look like figure 2 below Figure 2 Circuit with VOLTMETER and AMMETER Click the run button gt Wait for a few seconds then when you see the measurements on the VOLTMETER and AMMETER click stop Record your mea
45. ctron gun for producing a beam of rapidly moving electrons called cathode rays a fluorescent screen upon which a luminous spot is produced by the impact of the cathode rays and a means for displacing the spot from its quiescent position as the result of current or voltage applied to the deflecting mechanism Although the electron beam may be focused by means of magnetic fields electrostatic focusing is usually used Fig I shows the electrode structure of a typical cathode ray tube having an electron gun with electrostatic focusing Deflecting Electron Filament Heated Cathode Cylindrical Focusing Fluoresent Anodes Screen Figure 1 The electron gun consists of an electron source i e an electrically heated cathode which boils off electrons a grid G for controlling the intensity of the electron beam hence the brightness of the luminous spot and two anodes A and A2 The final velocity with which the electrons leave the gun is determined by the potential of A which is normally maintained constant The electrostatic fields between G and A and between A and A2 focus the stream of electrons in a 93 manner somewhat analogous to the focusing of light rays by lenses Usually the focus control on the oscilloscope adjusts the potential of A1 After leaving the electron gun the electron beam passes between a pair of horizontal plates A potential difference applied between these plates deflects the beam in a vertical pl
46. del 72 6805 OOWOOQOOOOOOO H his mam a eee Cem OOOOOOOO Figure 1 First Time Operation How To Produce The Bright Line Before turning on the power insert the plug of the power cord on the rear panel into the power supply wall socket and set the controls as follows POWER 1 OFF INTEN 6 Midrange FOCUS 3 Midrange VERTICAL MODE 21 CH1 ALT CHOP 12 Released ALT AC GND DC 11 12 GND VERT POSITION 19 20 Midrange VOLTS DIV 13 14 0 5V DIV VARIABLE 15 16 CAL Rotate fully clockwise In this case the VOLTS DIV is calibrated to its indicated value CH2 INV 39 Released TRIGGER MODE 35 AUTO TRIGGER SOURCE 31 CH1 TRIG ALT 40 Released SLOPE 41 TIME DIVISION 26 0 5 msec DIV HORIZ POSITION 29 Midrange SWP VAR 27 CAL Rotate fully clockwise X10 MAG 30 Released 100 After setting the switches and control knobs as mentioned turn ON the POWER A trace will appear on the screen in about 20 seconds Adjust the trace to the appropriate brightness and image sharpness with the INTEN and FOCUS control knobs respectively DESCRIPTION OF THE OSCILLOSCOPE CONTROLS AND CONNECTIONS 1 POWER SWITCH Main power switch of the instrument The unit is set ON wh
47. e in the pipe Answer 2 a What is the wavelength of the 1 overtone Answer b What is the wavelength of the 2 4 overtone Answer 3 If the frequency of the 4 harmonic is 290 Hz then what is the speed of sound in the pipe Answer 17 Laboratory 2 Speed of Sound in Air Adapted from Jerry Wilson Physics Laboratory Experiments 4 Ed pp 227 230 1994 Houghton Mifflin Company Purpose The purpose of this experiment is to use resonance to measure the speed of sound in air Introduction and Theory Sound is a vibration that travels through a medium as a wave The speed of sound indicates the distance the sound travels in a given amount of time In dry air at 20 deg C the speed of sound is 343 14 meters per second Speed of sound is used in determining the distance between the objects For example consider an echo which is the reflection of the sound wave on a barrier The barrier can be a wall or a canyon If we make a loud sound within a canyon the sound waves will hit the wall of the canyon and reflect back forming an echo The time delay between the shout and the echo corresponds to the time for the sound waves to travel to the canyon wall and back Measurement of this time will give an estimate of one way distance to the canyon wall For example if an echo is heard 2 80 seconds after making the noise then the distance to the canyon wall can be found as follows Distance v t 343 14
48. e or other emergency response services For your convenience these are posted at several locations near entry exit points around the room Each student must be familiar with all elements of fire safety alarm evacuation and assembly fire containment and suppression rescue and facilities evaluation Use caution when working with hot plates steam generators open flames and the heat lamps Laboratory walkways and exits must remain clear at all times Keep magnets away from computers computer disks and your wallet or anything containing a magnetic strip such as your ID or credit cards Be very careful when handling hot water do not touch the beaker the hot water the hot plate or any other container of hot water and ensure the hot plate does not get wet and wear gloves and or use tongs when handling containers that have hot water Glassware breakage and malfunctioning instrument or equipment should be reported to the Teaching Assistant or Laboratory Specialist It is best to allow the Teaching Assistant or Laboratory Specialist to clean up any broken glass All accidents and injuries MUST be reported to the Laboratory Specialist or Faculty teaching affected lab section An Accident Report MUST be completed as soon as possible after the event by the Laboratory Specialist No tools supplies or other equipment may be tossed from one person to another walk the item in question to the recipient and hand it to them Although the voltages and current
49. ear to diverge from the focal point Theory If the image is formed on the side of the lens opposite the object it is real and can be observed on a screen However if the image is on the same side of the lens as the object it is a virtual image and cannot be seen on the screen Analytically the thin lens equation and magnification factor are used with the sign convention similar to that in the following table These equations apply only to thin lenses The focal length of a lens is given by the lens maker s equation 1 1 1 F n 2 qh Where n is the index of refraction for the lens material and the R s are taken as positive for convex surfaces Lenses used in the laboratory are made from glass which has an n between 1 5 and 1 7 As an example for glass with n 1 5 and symmetrical converging lenses R R and R2 R the equation yields f R for f to be equal to R 2 for a symmetrical lens requires n 2 which is greater than the index of refraction of glass The focal length of a lens depends on the R values in general which can be different as well as n 88 Quantity Conditions Sign Focal Length f Convex Lens Concave Lens Object distance do Usually always in this experiment although there are some cases of lens combinations where d may be negative when an image is used as an object Image distance d Image real Image virtual Magnification M Image upright Image inverted Equipment Concave and C
50. ecialist to enter All visitors and invited guests MUST adhere to all laboratory safety rules Adherence is the responsibility of the person visited Location of PPE Personal Protection Equipment Safety goggles are kept in the drawer marked goggles A first aid kit is available near the sink toward the front of the lab room In addition the laboratory manuals contain elements of the above as they pertain to each particular experiment 11 Laboratory 1 Finding Absolute Zero Purpose The purpose of this exercise is to determine the absolute zero point and find the relation between pressure volume and temperature in a gas Introduction and Theory Boyle s law states that the pressure of a gas in a container is related to the volume of the gas In other words as the volume changes the pressure changes For a given amount of a gas at a fixed temperature the pressure of the gas is inversely proportional to the volume One way to verify this is to graph the inverse of gas volume versus gas pressure _ lll M The most common states of matter found on Earth are solid liquid and gas The only difference among all these states is the amount of movement of the particles that make up the substance What determines the state of matter is the random movement of the particles that comprise the substance relative to the intermolecular forces Temperature T is the measure of the average kinetic energy of the pa
51. ed in procedure 1 compute fo Si hr the focal length of the concave lens 90 Appendix A Computer Simulation Exercises Introduction One of the many conveniences of computers is their powerful ability to simulate natural phenomena Computer simulations save scientists billions of dollars per year by avoiding expensive experiments in wind tunnels and blast chambers as two examples Computer simulations can be performed to simulate a phenomenon that we cannot readily access such as the gas flows inside a star in the process of going supernova the fluctuations of an atom and the evolution of a solar system over billions of years time Back on Earth much simpler simulations can be used in the classroom to repeat live experiments using an array of initial conditions enabling students to see clearly how changing parameters can change the outcome of an experiment In this Lab we are going to run such a simulation The assignment which will vary by instructor and class section is to select an experiment of your choosing in the areas of Thermodynamics Electricity amp Magnetism Optics or Modern and run through that experiment several times virtually changing the initial conditions and recording the outcomes of each run Equipment Computer with Internet access the instructor will decide whether to use the website given below another website or a CD ROM simulation program OR Physics Computer Simulation Program found o
52. eld that opposes the change in magnetic flux through the area enclosed by the loop Again Faraday s law of induction is AP ae ee A BA cos 0 At At AB N Acos At where we assume a secondary coil coil 2 of N2 turns To generate our magnetic field we shall use a 200 turn Helmholtz coil coil 1 Along the axis perpendicular to the loop the magnitude of the magnetic field is _ uN 1 R Ux BR T m where u 47 x10 is the permeability of free space I is the current N is the number turns and R is the radius of the coil and x is the distance perpendicular along the coil axis A signal generator will provide a sinusoidal current to the primary coil to produce B Hence 2 UN Tmax Ri B B sin 2zft where B Ux R Y And N Acos o 27fN B A cos 0 cos 2 aft t 62 Laboratory 8 Report Sheet Magnetic Induction Experimenters Course Date Purpose The purpose of this experiment is to examine Faraday s law of induction which states that a changing magnetic flux produces an emf and electric current in a conductor Equipment Oscilloscope 1 Function Generator 1 Helmholtz Coils 1 pair with base Coaxial Cables 1 set Procedure Connect the experiment as shown below Oscilloscope Signal Generator Changing Magnetic Field 63 Data Calculate the magnetic field in coil 1 and coil 2 when it is 10 cm from coil 1 and both coil
53. en the switch is at the pushed in position 2 POWER LAMP This LED lights up when the main power switch is ON 3 FOCUS CONTROL Focus the trace to the sharpest image by turning this knob clockwise or counterclockwise 5 TRACE ROTATION Used to align the trace of the CRT with the horizontal graticule 6 INTENsity control Controls the brightness of the spot or trace Brightness is increased by turning the INTEN knob clockwise 7 POWER SOURCE SELECT SWITCH Line voltage selector used to select power sources 8 AC Inlet Connect the AC power cord supplied to this connector 9 CH1 INPUT Connector Terminal for the input signal to CH1 The input signal to CH1 is the X axis signal when the oscilloscope is used in X Y operation 10 CH2 INPUT Connector Terminal for the input signal to CH2 The input signal to this terminal becomes the Y axis signal when the oscilloscope is used in X Y operation 11 12 AC GND DC Selects the connection mode between the input signal and the vertical amplifier AC At this setting the DC component of the signal is cut off and only the AC component is displayed GND The vertical amplifier input is grounded and input terminals are disconnected DC At this setting the input signal is directly connected to the vertical amplifier and is displayed unchanged including the DC component 13 14 VOLTS DIV Selects the vertical axis sensitivity from 5mV DIV to SV DIV with 10 range
54. ent DC Power Supply 1 Resistor Box 1 Capacitor 100 uF 1 2 Position Switch 1 optional Data Studio w Voltage Sensor 1 Lead Wires 5 Alligator Clips 5 Procedure 1 Set the resistor box for a time constant T RC 1s e g if C 100 uF then R 10 KQ 2 Short the capacitor by connecting the leads together to ensure that it is not charged 3 Connect the circuit shown in Figure 1 with the switch at position B 4 Open Data Studio and connect to the voltage sensor Setting the sampling rate to 100 Hz will permit measurements of time constants greater than 0 1 s 5 Connect the Data Studio voltage sensor across the capacitor 6 Turn on the power supply and set the voltage not to exceed 8 V Do not saturate the power supply voltage 7 Start Data Studio to graph V vs t 8 Move the switch to position A to charge the capacitor 9 When the voltage plateaus V V move the switch to position A to discharge the capacitor 10 Stop Data Studio when the capacitor is nearly fully discharged V 0 and you are satisfied with the resulting curves If not satisfied repeat steps 8 and 9 until you are or start a new data set by repeating steps 7 10 11 Highlight the voltage rise charging and fit with an inverse exponential fit to obtain the time constant Print the fitted data noting the values used for the resistance and capacitance on the plot 12 Highlight the voltage decline discharging and fit with a natur
55. er to work with equipotential lines Having plotted sufficient equipotential lines we may then map out the electric field lines which are normal perpendicular everywhere to them If we know the potential at a discrete number of points which is what you will measure today then Ex AV Ax If the direction is along a field line which is perpendicular to the equipotential lines then in that direction along the field line E AV As where As is along the field line To the right is an example of two charges dipole and the associated electric field Note the equipotential lines dashed are everywhere perpendicular to the electric field The sketch on the next page displays the correct setup of the circuit we are working with We will have a 12V DC power supply connected to a board with conducting push pins which serve to affix the paper to the board and provide a conducting path for the electric current to flow into the paper 27 SAFETY NOTE It only takes 1 10 of an ampere 0 1 amp to kill a human being This power supply can output 5 10 of an ampere 0 5 amp Therefore it is important to make sure you remove power turn off the power supply when making any adjustments to the circuit 28 Laboratory 3 Report Sheet Electric Potential and Field Mapping Experimenters Course Date Purpose We will investigate the nature of electric field lines by mapping equipotential lines lines of constant
56. esseressetessresseesseesseresseeesseesseesseeesseeestts 107 Appendix D Magnetic Fields Laboratory Package n ssenesesesesesseessseesseesseesseresseeesseessresseeeseee 112 Introduction to this Document and the Labs Introduction This laboratory manual has descriptions of the laboratories which you will be doing this semester It also explains some of the concepts required to be understood in order to successfully complete this course and provides examples from everyday life illustrating the concepts This laboratory manual is the required reading material for this course The student you will be learning how to apply the scientific method in the laboratory setting Science is the study of the interrelationships of natural phenomena and of their origins The scientific method is a paradigm that uses logic common sense and experience in the interpretation of observations The underlying basis of the scientific method is to understand through repeatable experiments No theory is held to be tenable unless the results it predicts are in accord with experimental results A major problem is how does one quantify data so that experiments can adequately be compared Physicists try to apply a rigorous method of error analysis and then compare results with respect to the inherent experimental errors If two experiments produce results that are the same to within experimental error then we say that the experiments have validated each other
57. ettings then the x axis of display is time while CH 1 or CH 2 inputs give a vertical deflection The Lissajous figures can be used to calibrate the Function Generator Whenever a stationary pattern is achieved as the frequency is varied the frequency ratio of the vertical input to the horizontal input is equal to the ratio of the number of horizontal to vertical points of tangency to a rectangle that encloses the pattern or the ratio of the number of horizontal to vertical axis crossings Explain why this is true Note Fig 3 gives a rough sketch of the Lissajous pattern resulting from the X and Y input voltages shown In this case the frequency ratio f f 1 and the phase angle between the two sine waves is about 30 Assuming that the vertical signal is exactly 60 Hz check a few points on your Function Generator frequency reading e g 30 60 90 120 240 Hz and evaluate correction factors if any for them i e the number which must be added to the generator reading to obtain the actual frequency defined by your standard and the oscilloscope as a function of generator frequency The sine of the phase angle is given by sin A B as defined in Fig 3 Can you show this mathematically Does this relation uniquely define the phase angle in the range 0 277 Results Analog Oscilloscope Using the settings that were assigned in lab answer the following questions 97 9 Oy Su A What is the setting on the Volts
58. experiments m s Percent Error Unknown Primary Frequency Frequency Wavelength Distance m Ad m Wavelength st 1 resonance d 2 resonance 3 resonance h 4 resonance Show work for calculations 23 Pre Laboratory 3 Electric Potential and Field Mapping Name Course Date 1 The sketch shows cross sections of equipotential surfaces between two charged conductors that are shown in solid black 30 V 20 V a What is the potential difference between points B and E b At which of the labeled points will the electric field have the greatest magnitude c What is the electric field at point A magnitude and direction 2 The sketch on the back of this page shows cross sections of two conducting spherical shells a 5 0 cm b 0 50 m and V 100 V a Using dashed curves draw representative equipotentials around and between the spheres b Using solid curves and arrows draw the electric field lines c What is the charge on the left sphere d What is the potential at point P midway between the two spheres e What is the magnitude and direction of the electric field at point P midway between the two spheres 24 Laboratory 3 Electric and Potential Field Mapping Purpose We will investigate the nature of electric field lines by mapping equipotential lines lines of constant potential This lab will show you how to measure and
59. found by the four methods Attach a typed Conclusion section and a Discussion section Optional extension may be done alongside with or after the main experiment This is the Electronic Workbench exercise provided in the first part of the lab write up Extra Credit up to 3 pts can be obtained for the equivalent resistance analysis of the extra credit circuit 51 Pre Laboratory Exercise 6 RC Circuits Name Course Date 1 In a circuit such as the one in Figure 1 on back with the capacitor initially uncharged the switch S is thrown to position A at t 0 The charge on the capacitor is a initially zero and finally CE b constant at a value of Ce c initially C and finally zero d always less than Ce 2 In a circuit such as the one in Figure 1 with the capacitor initially uncharged the switch S is thrown to position A at t 0 The current in the circuit is a initially zero and finally amp R b constant at a value of amp R c equal to amp R d initially amp R and finally zero 3 In a circuit such as the one in Figure 2 the switch S is first closed to charge the capacitor and then it is opened at t 0 The expression V ge C gives the value of a the voltage on the capacitor but not the voltmeter b the voltage on the voltmeter but not the capacitor c both the voltage on the capacitor and the voltmeter which are the same d the charge on the capacitor 4 Ifa 5 00
60. frequency symmetrical about the resonant frequency Explain At resonance the reactances of the inductor and the capacitor cancel each other out so that the impedance Z is equal to just the resistance R Calculate the resistance of the circuit by using the amplitude of the current at resonance in the equation R V I Is the resistance equal to the used in the circuit Why not 80 Pre Laboratory Exercise 10 Reflection and Refraction of Laser Light Name Course Date 1 Light refracts when it travels from one medium to another Explain why What principle explains this behavior 2 Given that the speed of light in a given medium is 2 3 x 10 m s Find the index of refraction n for that medium For questions 3 5 consider the figure given above in which light fi 5 5 x 10 Hz travels from medium 1 to medium 2 The index of refraction for medium one and two are 1 2 and 1 6 respectively The angle of incidence 0 is 68 3 What is the frequency in medium 2 4 What is the velocity of light in medium 2 5 Find the angle of refraction 62 Show work 81 Laboratory 10 Reflection and Refraction of Laser Light Purpose The purpose of this laboratory exercise is to study the nature of reflection and refraction of laser light and find the index of refraction of the material used Introduction When a light beam falls on a surface both reflection from the surface and refraction into the subst
61. from the can to prevent overflow and spilling when the can becomes filled when lowering With the water level in the tube near the top take a tuning fork of known frequency and set it into oscillation by striking it with a rubber mallet or on a rubber block Hold the fork so that the sound is directed in the tube experiment with the fork and your ear to find the best orientation With the fork above the tube lower the reservoir can The water in the tube should slowly fall at this time and successive resonances will be heard as the level passes through the resonance length position It may be necessary to strike the fork several times to keep it vibrating sufficiently With the pattern of resonances approximately known adjusting the height of the water at each of the resonances in turn Record the height of the water for each resonance Since only the difference in height between resonances is used one can use the marks on the glass tube as a meter stick Repeat steps 2 and 3 with another tuning fork of known frequency Find the speed of sound and experimental error a Compute the average wavelength for each fork from the average of the differences in the tube lengths between successive anti nodes b Using the known frequency for each fork compute the speed of sound for each case 20 c Compare the average of these two experimental values with the value of the speed of sound given by the last equation by computing the percent error if thi
62. g source signal and the EXT TRIG IN input signal CH1 Select CH1 to get internal triggering source signal CH2 Select CH2 to get internal triggering source signal LINE Use the power line frequency signal as triggering signal EXT Obtain external trigger source signal by applying external signal to the EXT TRIG IN input terminal 33 33 EXT TRIG IN Input Terminal This input terminal is used for external triggering signal by setting the SOURCE switch 31 to the EXT position 102 34 LEVEL This knob is used to decide at which portion of the waveform should the sweep be started by setting the trigger level This helps to display a synchronized and stationary waveform 35 TRIGGER MODE Select Switch Trigger mode selection AUTO The oscilloscope is brought into automatic triggering sweep in which sweep is always conducted In the presence of a triggered signal normal triggered sweep is obtained and the waveform stands still In the case of no signal or out of triggering the sweep line will appear automatically This is the usual and convenient setting NORM Triggered sweep is obtained and sweep is conducted only when triggering is in effect No sweep line will appear in case of no signal or out of synchronization Use this mode when effecting synchronization to very low frequencies TV V Used for observing the entire vertical picture of television signal TV H Used for observing the entire horizontal picture of
63. h as its physical shape the type of material it is made of and the temperature The resistance of a wire is directly proportional to its length and inversely proportional to its cross sectional area A Re a A An analogy for this is the flow of water through a pipe The longer the pipe the more resistance to flow but the larger the cross sectional area of pipe the greater the flow rate or the smaller the resistance to flow The material property of resistance is characterized by the resistivity p and for a given temperature Resistivity is independent of the shape of the conductor and rearranging the previous expression gives the equation for resistivity p with units of Q m or Q cm 34 For a cylindrical wire the cross sectional area will be A nD 4 Thus using R V I _aVD P it p X ae v D I 2 35 Laboratory 4 Report Sheet Ohm s Law and Resistivity Experimenters Course Day Objective The objective of this experiment is to verify Ohm s law and determine the resistivity of copper and constantan wire Equipment Ammeter 0 0 5 A Voltmeter 0 3 V Rheostat 20 Q Battery or power supply Meter stick Micrometers or Calipers Conductor board or wires of various types lengths and diameters Se ja ji ji 1 set Procedure 1 Set up the circuit as shown below with one of the wires on the conductor board in the circuit Leave the rheostat set to the maximum resis
64. he charge the charge would be accelerated away from the junction In other word because the charge carriers in a conductor are free an electric field cannot be sustained within a conductor Therefore charge cannot accumulate at a junction 41 These rules can be used to determine the equivalent resistance of combinations of resistors in series and parallel Consider a simple series combination as diagramed below Schematic for a Series Circuit is shown on the next page Vo applied voltage A ammeter V voltmeter Rj resistor one R resistor two When some number of resistors are arranged in a circuit hooked together in a series connection as in the above diagram the sum of the voltage drops across the separate resistors must equal the applied voltage Vo Vi V2 Va Using Ohm s law V JR and the fact that the current in the circuit must everywhere be the same the voltage relation can be written IR IR IR IR where Rag is the equivalent resistance of the circuit Thus the total resistance in the circuit is the sum of the individual resistances Note that the ammeter has an internal resistance that needs to be included in this experiment R DR series When a set of resistors are arranged in parallel as in the diagram below the total current into the parallel part of the circuit is equal to the sum of the currents in each branch of the parallel circuit 42 Lata Using Ohm s law
65. he mouse over the icons and select FUNCTION GENERATOR Drag it closer to the other components and the left click Go back to the right side of the program and select OSCILLOSCOPE Drag it closer to the other components and left click Click on the edge of the components and use the wire to connect them The circuit should look like figure 1 below Ensure that the positive terminal of the function generator goes to the positive terminal of the ammeter Check the schematic in the figure 1 below to ensure that the terminal match your schematic Double click on the oscilloscope Then click run b or Coy Then click stop or Coy Pull the green vertical line that is on the left of the graph to the crest of the sine wave on the graph It will change color to yellow Then pull the red vertical line to the trough it will change to blue and record your results given by the yellow vertical line Your results should look like figure 2 below Double click on the function generator and change the frequency Run and stop the experiment and record your results Figure 1 RLC Circuit 13 Time Channel_A Channel_B 82 743ms 19 652 V Reverse 84 217 ms 19 732 V 1 474 ms 39 384 V save A Channel A Channel B Trigger Pscale 1 ms Div Scale 20 vidiv S scale 5 Wi Edge F IWE 9X pos Div 0 Y pos Div 0 Y pos Div 0 Level o y add ac Lo Jpc ac Lo eo Type 5ing Nor Buto None
66. here the north and south pole of the magnet is located III Pickup Coil Go to the Pickup Coil tab and investigate the equipment Explain 2 ways that you can get the light bulb to light What factors determine how brightly the light shines IV Transformer Investigate the setup of this experiment Run once with the battery powered DC current electromagnet to get the light bulb to shine Do it again with the AC current What do you notice that is different when the AC current is run versus the DC current 118 What else can you change about the pickup coil How does that change the outcome of the experiment V Generator What is happening in this experiment and how do things change with the changing flow of water Change out the light bulb for the meter How does the meter behave as you change the flow of water that drives the generator How does this demonstration relate to the power generation methods of some locations in the U S Write your responses after each section of the simulation sequence 119 Lab 8 Report Sheet Magnetic Fields Experimenters Course Date Part 1 Magnetic field of bar magnet attached Part 2 Measure the Earth s magnetic field Part 3 Field strength along axis of a Helmholtz coil Data Tables N of turns R radius V voltage B measured B theoretical Difference 120 Attach a plot of the measured B versus x Summary Attach a
67. his calculate the percent difference between the measured and the calculated values How does the field drop off as you move away from the coil you may wish to plot this to get a better idea of this 116 B sie Zn Beas diff 100 calculated Data and Results Attach the map s of the magnetic field s you made from Part I to this write up If you mapped two fields how were they similar How were they different Did all of your field lines make closed loops Material from the computer simulation section can go on the back of this sheet if this activity is performed You may use the following data sheet or construct your own or use an alternative one provided by your instructor Solenoid observations The 800 turn coil Radius N I R R m B field Measured B field Difference Calculated center 2R 3R 5R 10R 117 3 Computer Simulations Optional Extension to the Lab If instructed by your professor you will do a simulation that is provided by the University of Colorado s Simulation Library Go to Faraday s Electromagnetic Lab on the following website http phet colorado edu simulations sims php sim Faradays_Electromagnetic_Lab Click on run now to launch the simulation you may need to press the Ctrl button as you click run to enable the popup window to appear There are five tabs for five activities bar magnet pick up coi
68. in the form y a bx and we usually read from left to right The first variable goes along the ordinate i e the vertical axis and the second is placed along the abscissa 1 e the horizontal axis 4 Use a meaningful graph title Use meaningful axis titles that include the units of measurement 5 Use appropriate scales for the axis that are easy to read and will allow the data to most nearly fill the entire graph Do not use categories as axis labels If practical include the origin that is the point 0 0 at the lower left of the graph However the origin should be suppressed if the data is bunched a long way from zero 6 Take a set of data points by measuring a value for y for each given value of x 7 Draw the best fit straight line the line that most nearly goes through all the points Half the points should be above the line and half should be below the line Do not force the line to go through the origin Unless 0 0 is a measured data point 8 Example graph next page Calculation of Velocity y 1 13 1 01 x Position 5 in Meters 0 2 4 6 8 10 Time in Seconds s Ad _ 6 9 m 1 0m Tore Slope rr y 7 re ae 1 02 m s 9 Slope calculations e Use a large baseline on the graph to find the Ax and Ay values e A large baseline will increase the accuracy of your calculations e In general you should do the slope calculations on the graph e Draw the baseline along some convenient ordinate starting from
69. ion amp Theory When an inductor L a resistor R and a capacitor C are connected in series the alternating current I present in the circuit depends on the frequency of the driving voltage E This type of circuit is used extensively in electronic devices particularly radios and televisions These circuits are used in a number of electronics applications including the tuning of analog radios and televisions Adjustable tuning is usually achieved by using a parallel plate variable capacitor which enables the value of C to be changed which enables the receiver to tune to stations of different frequencies The inductor comes with an adjustable core which enables the inductance L to be changed The core is made of a high permeability material that effectively increases inductance and is threaded so that it can be screwed in or out of the inductor winding as needed Filters are another common use of RLC circuits In a filtering application the resistor R becomes the load that the filter is working into The damping factor value is selected based on the desired bandwidth of the filter A wider bandwidth uses a larger damping factor and vice versa The three components of the circuit give three degrees of freedom to the designer of the circuit to enable the desired outcome to be met Two of the components are required to set the bandwidth and the resonant frequency the third can be adjusted in such a way so as to scale each of the three components to con
70. is conservative and we can define a potential energy APE AW We define an electric potential V as the potential energy per unit charge The potential difference AV as a charge moves from point a to point b is AV Vp Va APE q AW q E As Hence APE gAV qEsAs and the potential energy of a charge q in an electric fieldis PE qV If As is in the direction of E then g AV AS Indeed any component of E is just E AV Ax For example Ex AV Ax and E AV Ay Paths of constant potential are called eguipotentials The electric field is everywhere perpendicular to equipotentials points from high to low potential and its magnitude in V m N C is just the potential difference divided by the distance along the field 26 The properties of conductors are fully represented by the notion of electric potential Recall that for a static conductor 1 The electric field is zero inside a conductor This implies that the potential is the same everywhere inside and equal to its value at the surface 3 All excess charge must reside on its surface and is distributed according to the shape of the conductor the surface charge density o is greater where the curvature is greater 4 The electric field is normal perpendicular to the surface and its magnitude at the surface is o 2 amp 5 We can map electric field lines by determining either 1 The lines of force or 2 Equipotential lines It is easi
71. ission gratings Place each available grating one at a time between the laser and wall and note the pattern of dots on the wall How does the pattern change with each different grating You do not have to take measurements just a qualitative observation should be sufficient Record your response in the Discussion section of your lab report 87 Laboratory 12 Concave and Convex Lenses Adapted from Jerry Wilson Physics Laboratory Experiments 4 Ed pp 471 475 1994 Houghton Mifflin Company Purpose The purpose of this experiment is to investigate the optical properties of convex and concave lenses Introduction Mirrors and lenses are familiar objects that we use on a daily basis The most commonly used mirror is what is called a plane mirror which is used for cosmetic applications Spherical mirrors have many common applications such as security monitoring of store aisles and merchandise and concave spherical mirrors are used as flashlight reflectors Mirrors reflect light while lenses transmit light Spherical lenses are used to converge and focus light convex spherical lenses and to diverge light concave spherical lenses This experiment will focus on spherical lenses of two types convex and concave Convex lenses are sometimes called converging lenses because rays parallel to the principle axis converge at the focal point A concave lens is called a diverging lens because rays parallel to the perpendicular axis app
72. ith a green laser instead of a red one Try to keep the orientation identical to that of the red laser or better yet shine them side by side Are they reflected differently Do they refract differently What is the index of refraction as determined by the green laser and how does it compare with that determined by the red laser 85 Laboratory 11 Laser with Diffraction Grating Adapted from Halliday Resnick Walker Probe ware Lab Manual 6 Ed pp 182 183 2003 John Wiley amp Sons Inc Purpose The purpose of this experiment is to investigate the optical properties diffraction gratings using a laser Safety Note Do not stare into the aperture opening where the light comes out of a laser at any time Exposure to the laser light could result in permanent eye damage Introduction amp Theory When monochromatic light from a distant source such as a laser passes through a narrow slit then falls on a viewing screen the light produces on the screen a diffraction pattern This pattern consists of a broad and intense very bright central maximum and a number of narrower and less intense maxima secondary maxima Minima lie between the maxima A Light Sensor measures the intensity of this pattern the Rotary Motion Sensor mounted on the Linear Translator measures the relative positions of the maxima in the pattern The diffraction pattern for a single slit is similar to the pattern created by a double slit but the central
73. l electromagnetic transformer and generator We will do all five Answer all the questions posed in the five activities below in the discussion section of your laboratory report I Bar Magnet On the screen you should have a bar magnet and a compass 1 Compare the magnetic field around the bar magnet represented by the little arrows to the electric field around a positive and negative charge 2 Use the magnetic field sensor to find the strength of the magnetic field at 8 points spread out around the magnet Sketch the magnet and at these points draw a vector with size and direction that represents the field 3 Use the magnetic field sensor to find the magnetic field inside the magnet Explain your findings 4 Measure the magnetic field strength at 10 points along a straight line extending out from the magnet s south pole As there is no measuring tape on this simulation use a ruler against the screen to measure distance in cm Make a graph of magnetic field vs distance attach to this write up II Electromagnet Go to the Electromagnet tab 1 Sketch the electromagnet Label the parts and show what is happening in the electromagnet to create a magnetic field 2 How does the magnetic field compare to that of a bar magnet 3 What things can you change in the simulation that affects the magnetic field List the options and explain the resulting change in the field 4 What physical factor in the electromagnet determines w
74. lder With no current flowing determine the mass of the Magnet Assembly Record this value in the g g y first column under Mass in Table 3 1 on the appropriate line Set the current to 2 0 amps Determine the new mass of the Magnet Assembly Record this value in the second column under Mass in Table 3 1 Subtract the mass you measured when there was no current flowing from the value you measured y g y with current flowing Record this difference as the Force Add additional magnets one at a time Make sure the north poles of the magnets are all on the same side of the Magnet Assembly Each time you add a magnet repeat steps 3 5 If you use an electronic balance Usea single magnet centered under the center of the holder Place the magnet assembly on the pan of the balance With no current flowing press the TARE button bringing the reading to 0 00 grams Now turn the current on and adjust it to 2 0 amps Record the mass value in the Force column of Table 3 1 Add additional magnets one at a time Make sure the north poles of the magnets are all on the same side of the Magnet Assembly Each time you add a magnet repeat steps 3 5 Data Processing Plot a graph of Force vertical axis versus Number of Magnets horizontal axis Analysis What is the relationship between these two variables How does the number of magnets affect the force between a current carrying
75. led out PULL CMOS a CMOS signal is present at the TTL CMOS jack Turning the control clockwise increases the amplitude and turning the control counterclockwise decreases amplitude amplitude is adjustable from approximately 4 V p p to 14 5 V p p 8 OFFSET Control When control is pushed in DC offset is set at zero When control is pulled out PULL ADJ clockwise rotation changes DC offset in a positive direction and counterclockwise rotation changes DC offset is a negative direction Full clockwise rotation gives approximately 5 V into 50 load 10 V open circuited Full counterclockwise rotation gives approximately 5 V into 50 load 10 V open circuit 10 DUTY Control Rotation adjusts the duty cycle of both the main OUTPUT signal and the TTL CMOS signal Fully counterclockwise rotation is the CAL position normal duty cycle Duty cycle changes when control is rotated away from CAL position When control is pulled out PULL INV the square wave at the main OUTPUT and the TTL or CMOS signal are inverted 12 COARSE Frequency Control Coarse adjustment of output frequency main output and TTL CMOS output from 2 to 2 times the selected range 14 Hz and kHz LED Indicates whether display is showing Hz or kHz 105 Figure 2 E gt exc rmeceson sone oiik outs FUNCTION GENERATOR CT 035 Feo teas 2 n 8 8 7 6 5 106 APPENDIX C Experiments in Magnetic Force with PASCO s Basic Curre
76. ll safety instructions including those posted on the wall of the room you are in if additional special safety guidelines are needed they will be printed for each lab needing them Each student student assistant and instructor that uses the lab is required to receive a safety briefing before beginning laboratory exercises More details on laboratory safety for Physics II laboratories are provided in the next chapter of this Laboratory Manual Laboratory Safety Information Safety in the laboratory is very important The experiments performed in the laboratory are designed to be as safe as possible but caution is always advised concerning the use of the equipment When you arrive at the start of each class meeting it is very important that you do not touch or turn on the laboratory equipment until it has been explained by the professor and permission has been granted to get started The equipment for the labs are set up for you in advance so resist the urge to play with the equipment when you arrive as you may hurt yourself or others or damage the equipment While the experiments done in Physics II primarily electricity and magnetism are generally safe it is always important to be cautious when using equipment especially if you are unfamiliar with the equipment If you have any questions about the safety of a procedure or of the equipment ask your instructor before handling the equipment Some specific exercises in the laboratory do pose
77. low The function generator will apply the voltage to the circuit at different frequencies The oscilloscope will measure the voltage across the resistor Record the data in the table Plot a graph of V vs linear frequency f Determine the inductive reactance Capacitive reactance impedance and amplitude of the current through the resistor and plot Xz vs frequency f Xcvs f and Z vs f 4 Refer to the Analyzing the data section on the image below 69 Oscilloscope cable from black Function generator black red Analyzing the data 1 From the graph find the linear resonant frequency fres Using the resonant frequency fye calculate the resonant angular frequency Oes and record the value in the Table 2 3 Calculate the theoretical resonant angular frequency using the values of the inductance and capacitance 4 Compare the theoretical resonant frequency to your measured resonant frequency N 70 Results Complete Table 1 Linear Frequency V V X 2a Q 1 Ea 9 Z Q Ve I 0 71 Complete Table 2 Below Parameter Name Parameter Value Inductance Resistance Capacitance Resonant Frequency linear Resonant Angular Frequency Theoretical Resonant Angular Frequency Conclusions amp Questions 1 How does the measured value
78. m and b minimum a b 2 A 2 T uniform magnetic field makes an angle of 30 with the z axis The magnetic flux through a 3 m portion of the x y plane is Show your work 3 Faraday s law states that an induced emf is proportional to the a rate of change of magnetic field b rate of change of electric field c rate of change of magnetic flux d rate of change of electric flux 4 In an experiment two coaxial coils are used to investigate induction A sinusoidal current is passed through the first coil The induced emf in the second coil does not depend on the a frequency of the current b number of turns in coil 2 c area of coil 2 d resistance of coil 2 e amplitude of the current in coil 1 60 Laboratory 8 Magnetic Induction Purpose The purpose of this experiment is to understand how changing magnetic fields can produce electric currents In doing so we examine Lenz s Law and Faraday s Law Introduction and Theory Magnetic flux is defined as the product of magnetic field lines and the area through which they pass Of importance is that the total magnetic flux through a closed surface is zero This implies that monopoles do not exist The magnetic flux is dependent on the strength of the magnetic field the size of the area through which they pass and the angle between the normal of the area and the magnetic field We will investigate the dependence of flux on these variables and how a
79. mat Group Number Date Group Members Object What is to be done in this experiment Apparatus Apparatus used to perform the experiment Theory The calculation equations used along with meaning of the symbols and units used Equations can be neatly hand written Data Raw data in tables should be placed in this section Sample calculations should be shown Error calculations should be shown Discussion Include a discussion of some of the sources of experimental error or uncertainty If appropriate should also include a comparison of various experimental errors For example We found that our value of the density within one standard deviation has a range of 2 68 to 2 78 x10 kg m The quoted value of the density for aluminum falls within this range and no other material densities fall within this range so our cylinder appears to be made of aluminum Conclusion Short but comprehensive Was the object of the experiment met 7 For example The density of the cylinder was found to be 2 73 0 05 x10 kg m We selected aluminum as the material composing our cylinder because the density of aluminum 2 70 x10 kg m is within the experimental error of our calculated density Safety Reminder It will be necessary to follow procedures to ensure safety in each lab Most labs do not present any significant danger but some will require certain safety measures to be followed The general recommendation is to follow a
80. maxima is measurably brighter than the maxima on either side Analysis of wave diagrams for light of wavelength passing through a single slit with width a gives the following general equation asin mA where 9 is the angle of the first dark fringe on either side of the central maxima The dark fringes can be located with the general equation for m 1 2 3 relating wavelength A the number of fringes m and the slit width a Analysis of wave diagrams for light of wavelength passing through a double slit with slit spacing d gives the following formula dsin mi The bright fringes can be located with this equation Equipment Optical Bench 1 Diode Laser 1 Single Slit and Multiple Slit accessories 1 each Lens mount and screen 1 each Transmission gratings 200 300 600 13 400 lines mm 1 each Procedure 1 The apparatus should already be set up for you Make sure the lens bracket and laser are close to one end of the bench with the white screen near the other 86 2 Rotate the SLIT SET disk the Single Slit one on the Slit Accessory until a slit pattern is in line with the laser beam Use the 0 04 mm slit Use the adjustment screws on the back of the Diode Laser to adjust the beam if necessary 3 Examine the diffraction pattern on the white screen If the pattern is not horizontal loosen the thumbscrew on the Slit Accessory Slowly rotate the Slit Accessory until the laser beam is centered on the slit pat
81. minor safety risks e g labs that deal with electric circuits and guidelines related to these are presented with the write up for these particular labs In fact for many of the experiments the laboratory write up contains a section on safety specific to that activity the safety section should be read prior to starting the experiment and followed carefully throughout When an electric circuit is involved it is vital that you do not power a circuit until you verify with the instructor that it is set up correctly and then only when the instructor gives the go ahead to do so Not following instructions may result in personal injury damage to the equipment or both Although we do not use chemicals in the physics laboratories we do use dry ice and liquid nitrogen both of which present hazards do to their extreme coldness Extra caution is strongly advised when using these substances You will be dipping a constant volume pressure apparatus into dry ice then liquid nitrogen each of which will have a student laboratory assistant or faculty member stationed so as to prevent accidents Be careful not to splash any liquid nitrogen on yourself or touch any of it or the dry ice as severe frostbite could result In addition to the electricity and the cold materials other hazards may come from broken glass or thermometers in the event of such these should be cleaned up by the laboratory assistant or the instructor Safety is important for the equipment a
82. mula Experimental Errors There are two kinds of errors 1 systematic associated with particular measurement techniques improper calibration of measuring instrument human reaction time is the same error each time This means that the error can be corrected if the experimenter is clever enough to discover the error 2 random error unknown and unpredictable variations fluctuations in temperature or line voltage mechanical vibrations of the experimental setup unbiased estimates of measurement readings isa different error each time This means that the experimenter cannot correct the error after the data has been collected These errors can be made in two ways 1 Personal from personal bias or carelessness in reading an instrument e g parallax in recording observations or in mathematical calculations 2 External from the natural limitations of the physical devices Examples are old and misused equipment finite accuracy of measurement devices heat flow extraneous electric fields vibrations etc Accuracy how close to the true value is the result Precision how much spread is in the data e the more precise a group of measurements the closer together they are e high precision does not necessarily imply high accuracy Significant Digits 1 exact factors have no error e g 10 O 2 all measured numbers have some error or uncertainty this error must be calculated or estimated and rec
83. n the laboratory computers Instructor will give specifics Procedure There is a large number of simulation packages available from CD s and DVD s in the Physics Learning Center NSCI 324 to websites that offer applets and downloads that demonstrate various principles of physics For this experiment we will choose one such simulation within the areas mentioned above from a website to be determined Go to the website provided in class and click on one of the choices in the list The list includes simulations in the following areas Archimedes Principle The Ideal Gas Law The Kinetic Theory of Gases The Carnot Cycle and the Efficiency of Engines PP Physics in Practice Gasoline Engines Hooke s Law Damped Harmonic Motion 91 Pulses on a Rope Sound Waves The Doppler Effect Standing Waves on a String Beats Superposition of Electric Fields Electric Resistance and Ohm s Law Applications of Kirchhoff s Rules Magnetic Forces on Moving Charged Particles Generators and Motors Electromagnetic Waves The RC Circuit R L C Series Circuit Models of Light Rays and Waves Reflection and Refraction Thin Lenses Locating Images by Ray Tracing The Thin Lens Equation Reflection and Refraction of Light Waves Interference of Light Dispersion Crystals and X Ray Diffraction Spectroscopy The Photoelectric Effect Successes of the Bohr Theory Tunneling or Barrier Penetration Colors by Addition and Subtraction The pn j
84. nductors Capacitor Resistor Re NOR Re Procedure Setup the circuit as shown below The function generator will apply the voltage to the circuit at different frequencies The oscilloscope will measure the voltage across the resistor Record the data in the table Plot the graph of V vs linear frequency f Determine the inductive reactance capacitive reactance impedance and amplitude of the current through the resistor and plot X Xc and Z vs frequency f Refer to the Analyzing the data section on the image below 11 RLC Circuit Analyzing the data From the graph find the linear resonant frequency fres Using the resonant frequency fes calculate the resonant angular frequency es and record the value in the Table 2 Calculate the theoretical resonant angular frequency using the values of the inductance and capacitance Compare the theoretical resonant frequency to your measured resonant frequency 78 Results Complete Table 1 Linear V V X 2 Q 1 Z 9 Z quency 2afC Z Complete Table 2 Below ITEM VALUE Inductance Resistance Capacitance Resonant Frequency linear Resonant Angular Frequency Theoretical Resonant Angular Frequency 79 Conclusion amp Questions How does the measured value for the resonant angular frequency compare to the theoretical value for the resonant angular frequency Is the plot of impedance current versus
85. nerator Set the horizontal sweep i e TIME DIV for 5 ms cm turn the vertical gain i e CH 1 VOLTS DIV up high so that you can see very small signals and touch your finger to the center wire of the BNC cable without touching the grounded outer cable Adjust the vertical gain until you see a wave pattern with a few centimeters amplitude Measure the period of the wave and deduce its 96 frequency Identify the source of the signal for which your body is serving as an antenna Hint What else has that frequency What is the AC output voltage of your body antenna C Lissajous Figures i 5 Now set the horizontal sweep i e the TIME DIV i Vertical Deflection knob at the position X Y Then connect the Channel 2 input ZO to the transformer small yellow box which is plugged into the AC line power of the laboratory This box serves as a 60 Hz reference standard The electron beam of the oscilloscope is now displaced vertically by a sinusoidal potential at a frequency of 60 Hz Connect the Sine Wave output of the Function Generator to the horizontal input of Channel 1 9 Observe the various stationary Lissajous patterns which occur as the frequency of the signal generator is varied Figure 3 Horizontal Deflection Note If TIME DIV is set on X Y then the CH 1 input voltage results in a horizontal x deflection and a CH2 input voltage gives a vertical y deflection However when TIME DIV is at any of the time s
86. ng the lens equation compute the image distance and the magnification factor d Compare the computed value of d with the experimental value by computing the percent difference 89 Case 2 do R Repeat the procedure for this case Case 3 f lt dg lt R Repeat the procedure for this case Case 4 do lt f Repeat the procedure for this case It is initially instructive to move the lens continuously toward the object light source decreasing d from a d gt 2f and to observe the image on the screen which also must be moved continuously to obtain a sharp image In particular notice the change in the size of the image as do approaches f Concave Lens 5 Sketch ray diagrams for objects at 1 do gt R 2 f lt do lt R and 3 do lt f and draw conclusions about the characteristics of the image of a convex lens Experimentally verify that the image of a convex lens is virtual i e try to locate the image on the screen 6 It is possible to determine the focal length of a concave lens experimentally by placing it in the contact lens combination has a focal length fe given by 1 1 1 ee a fs Si Se Place the concave lens in contact with the convex lens convex surface to concave surface in a lens holder and determine the focal length of the lens combination f by finding the image of a distant object Record the results in the Laboratory Report Using the equation E with the focal length of the convex lens determin
87. ns for Discussion 1 Calculate the electric field for at least 2 illustrative locations on each conducting sheet Explain how you got your result and show the work 2 In a uniform electric field the potential changes from 3 5V to 4 2V when the probe is moved in 3 the x direction from 5 8 to 6 75 8 in units of cm Calculate the x component of the electric field between those points Show your work Attach your graphs to this report Attach a typed Summary 30 Food for thought 1 What is meant by potential difference 2 How does electric potential compare to other potential energies 3 What is an electric field 4 What do you notice of the shape of the equipotential lines in comparison to the shape of the electrodes 5 Why are electric field lines drawn perpendicular to equipotential lines 6 What is the polarity of the E field in your experiment 31 Science First 32 Pre Laboratory 4 Ohm s Law and Resistivity Name Course Date The characteristics of five wires are given in the table Wire Material Length Gauge A iron 2 0m 22 B copper 2 0m 22 C copper 2 0m 18 D copper 1 0m 18 E Tron 2 0m 18 The gauge is a measure of the diameter of the wire and 18 corresponds to a diameter of 1 2 x 10 m and 22 corresponds to a diameter of 6 4 x 10 m The resistivity of iron is 9 7 x 10 Q m and the value for copper is 1 72 x 10 Qm
88. nt Balance and Current Balance Accessory Main Unit Ring Stand SF 8608 Accessory Unit SF 8607 Basic Current Balance SF 8608 Current Balance Accessory What follows are four experiments one of which can be used for the Magnetic Force Experiment These experiments come courtesy of PASCO scientific who have provided the equipment and the user s manual which contain these experiments Experiment 1 Force versus Current Procedure If you re using a quadruple beam balance Set up the apparatus as shown in figure 1 1 Determine the mass of the magnet holder and magnets with no current flowing Record this value in the column under Mass in Table 1 1 Set the current to 0 5 amp Determine the new mass of the magnet assembly Record this value under Mass in Table 1 1 Subtract the mass value with the current flowing from the value with no current flowing Record this difference as the Force Increase the current in 0 5 amp increments to a maximum of 5 0 amp each time repeating steps 2 4 If you re using an electronic balance Set up the apparatus as shown in figure 1 1 Current Loop Magnet Assembly id Baie Main Unit Lab Stand Figure 1 1 Equipment Setup Place the magnet assembly on the pan of the balance With no current flowing press the TARE button bringing the reading to 0 00 grams Now
89. nts V 0V V NV V WV NA NA V tv V 0v Current measurements I 6 LEd NA L NA Data Analysis Series Circuit Equivalent resistance from ohmmeter Ra R R R Measured R Rq Resistance from Ohm s law OR OR OR OR OV oO kel R r Z I 1 I V R OR R 2 y eoh I V o pei OR R AL 2 j I V I o V ol oie alae R R R R OR OR OR OR Parallel Circuit Include R in series if needed Resistance from ohmmeter ee R R R OR 5 R R _ 1 R R 7 1 a R R RER Measured Ra R Resistance from Ohm s law OV Ol R OR R I V L V l R OR R ATSE E I V I ov A Rama R Ry 7 RR OR R R OR 5 R R 1 R R 7 1 a R R RER 50 Extra Credit Include R in series if needed Resistance from ohmmeter R RDR RR oR R eq a R R R R RER _ R R R R Measured R Rg Resistance from Ohm s law E m r 2 I Vo L pobe ae r Zea I 2 I ee R R 2 4H L V L RR OR 6R R OR OR O R R RR a RR RER V V l T we k Mer Summary For each circuit compare Req
90. of the index of refraction 3 What are some sources of error 4 Do you have enough information to determine the type of material the block is made of assuming the table above was not provided Why or why not 5 Round off your final answer correctly with respect to the amount of error 6 Write up your report in the usual manner remembering to answer all questions Bonus 1 Calculate the value of the speed of light inside the object used for refraction Bonus 2 Given that the wavelength of the helium neon laser light is 632 8 nm what material is the object used for refraction made of Extensions Because of the brief nature of this lab it is likely that your instructor may include some additional steps to provide more opportunity to explore the reflection and refraction of light These steps may include but are not limited to Using the table provided in the Introduction and the physical appearance of the object used to determine the index of refraction identify the material out of which your block was made of Repeat the experiment but also trace the reflected beam as well as the refracted beam Measure the reflected beam s angle to the normal along with the incoming beam s angle relative to the normal What do you notice Repeat the experiment with two or three other substances to include a plastic container filled with water a slab of glass or anything else we may find in the storage room Repeat the experiment w
91. onvex Lenses one of each 1 Convex Lens focal length longer than 1 convex lens 1 Meter stick optical bench white cardboard can serve as the screen or precision PASCO bench with lens holder and 1 white screen Light Source candle and candleholder or electric light source with object arrow Procedure Convex Lenses 1 Sketch a ray diagram for a convex lens with the object at its focal point The image is formed at infinity 2 using the lens equation determine the image characteristics for an object at infinity 3 Experimentally determine the focal length of the lens The lens may be placed in a lens holder and mounted on a meter stick 4 Solve cases 1 to 4 Case 1 d gt R Sketch a ray diagram for an object at a distance slightly beyond R i e do gt R and note the image characteristics a Set this situation up on the optical bench with the object placed several centimeters beyond the radius of curvature known from f determination with R 2f Measure the object distance do and record it It is usually convenient the lens manually and adjust the object distance by moving the lens rather than the object light source Move the screen along the side of the optical bench until an image is observed on the screen This is best observed in a darkened room The lens may have to be turned slightly to direct the rays toward the screen Estimate the magnification factor M and measure and record the image distance dj c Usi
92. orded with every final expression in a laboratory report the degree of error depends on the quality and fineness of the scale of the measuring device 3 Use all of the significant figures on a measuring device For example if a measuring device is accurate to 3 significant digits use all of the digits in your answer If the measured value is 2 30 kg then the zero is a significant digit and so should be recorded in your laboratory report notes keep only a reasonable number of significant digits e g 136 467 12 3 148 8 units e g 2 3456 0 4345634523 units gt 2 3 0 4 units NOTE hand held calculators give answers that generally have a false amount of precision It is good practice to ensure that you round these values correctly As a rule the final answer should have no more significant digits than the data from which it was derived Graphing Techniques 1 Graphs are either to be done on a computer using either Excel or the graphing utility of Data Studio or on quadrille lined paper for example engineering paper 2 We draw graphs for the following reasons e to see the functional dependence that is does it look like a straight line a curve or random data e to average out the data e to fit data to the linear hypothesis that is the data is of the form y atbx 3 You will be asked to plot a graph of the form y versus x We say y versus x rather than x versus y because we write the equation
93. per as shown Which one of the following phrases most accurately describes the motion of the electron once it has entered the field a upward and parabolic b upward and circular c downward and circular d upward along a straight line e downward and parabolic 2 An electron is moving with a speed of 3 5 x 10 m s when it encounters a magnetic field of 0 60 T The direction of the magnetic field makes an angle of 60 0 with respect to the velocity of the electron The magnitude of the magnetic force on the electron is Show your work 3 A 0 150 m wire oriented horizontally between the poles of an electromagnet carries a direct current of 12 5 A The angle between the direction of the current and that of the magnetic field is 25 0 If the magnetic field strength is 0 625 T what is the magnitude and direction of the magnetic force on the wire between the poles Show your work NOTE The Magnetic Force Lab if it is performed will be done using the Instruction Manual and Experiment Guide for the PASCO Scientific Model SF 8607 and SF 8608 Basic Current Balance and Current Balance Accessory Hard copies are available in the drawers where lab forms are kept and a soft copy version is appended as an appendix to this document 59 Pre Laboratory Exercise 8 Magnetic Induction Name Course Date 1 The magnetic flux through a surface is defined as BAcos At what angle is the magnetic flux a maximu
94. rticles Specifically oe Lar or KE 2kT 3k 2 2 Particles with a large kinetic energy tend to collide frequently and move apart Intermolecular forces tend to pull particles toward each other In an ideal gas there are no intermolecular forces In practice an ideal gas is sufficiently dilute that collisions are infrequent and the intermolecular forces are not effective Real gases at room temperature and pressure behave as if their molecules were ideal However at high pressures or low temperatures intermolecular forces can overcome the kinetic energy of molecules and the molecules can capture one another For an ideal gas kinetic theory can be used to show that the pressure of a gas is proportional to the number of molecules per unit volume and to the average translational kinetic energy of the lea E molecules 5m As defined above temperature is a measure of the average kinetic energy Thus one obtains the ideal gas law namely PV NkT 12 where k 1 38 x 10 J K is Boltzmann s constant P is the gas pressure V is the gas volume T is the temperature in degrees Kelvin and N is the number of molecules Note dividing both sides by the volume one obtains P nkT where n is the density When T and N are held constant one sees that 1 Po y Boyle s law When P and N are held constant one obtains V T Charles law At very low temperatures the intermolecular spacing decreases for real
95. s are parallel to each other Use Ohm s law V JR to obtain the current Show work Y R Bealculated_1 tesla Bealculated_2 tesla Complete Table 1 Below For ease you may record peak to peak voltage Angle Distance Frequency Voltage 1 Voltage 2 V V degrees between Coil 1 Volts Volts Coils Hz 0 10cm 200 Hz 10 10cm 200 Hz 20 10cm 200 Hz 30 10cm 200 Hz 40 10cm 200 Hz 50 10cm 200 Hz 60 10cm 200 Hz 70 10cm 200 Hz 80 10cm 200 Hz 90 10cm 200 Hz 100 10cm 200 Hz 110 10cm 200 Hz 120 10cm 200 Hz 130 10cm 200 Hz 140 10cm 200 Hz 150 10cm 200 Hz 160 10cm 200 Hz 170 10cm 200 Hz 180 10cm 200 Hz Make a graph of the induced voltage V2 versus angle 64 a What is the shape of the induced voltage in coil 2 versus angle b Is this what you expected and why c What is observed of the frequency in coil 2 How does it compare to the frequency in coil 1 What does this tell you d At 0 what is the peak voltage in coil 2 What did you expect for this value Complete Table 2 Below For ease you may record peak to peak voltage Angle Distance Frequency Voltage 1 Voltage 2 V V degrees between Coil 1 Volts Volts Coils Hz 0 3cm 150 0 4cm 150 0 6cm 150 0 8 cm 150 0 10cm 150 0 12cm 150 0 14cm 150 0 16cm 150 0 18 cm 150 0 20 cm 150 Make a graph of
96. s error is large you may have observed the resonances of the tuning forks overtone frequencies consult your instructor in this case Data h height of water at resonance 4h distance between successive resonances Casel f Case2 f h Ah h Ah Ah Ah V 2f Ah Vs 2f Ah Average vs T vs 331 5 0 67 m s difference Attach typed Conclusion and Discussion sections 21 Data Sheet 1 Primary Frequency Frequency Wavelength Distance m Ad m Wavelength st 1 resonance d 2 resonance d 3 resonance th 4 resonance Show work for calculations Average Calculated Wavelength Calculated Speed of Sound in air 2 Primary Frequency Frequency Wavelength Distance m Ad m Wavelength st 1 resonance d 2 resonance d 3 resonance th 4 resonance Show work for calculations Average Calculated Wavelength Calculated Speed of Sound in air Recorded room temperature C The theoretical speed of sound in air is approximately 343 m s at 20 C Determine the theoretical speed of sound in this classroom based on you temperature readings Theoretical speed of sound in air in this classroom m s Averaged speed of sound in air from your
97. s in position A the capacitor will charge When charging a capacitor with a DC source V the voltage V and charge Q will increase over time The voltage is characterized by the equation VA V d e V l e If t RC 7 then the equation reduces to Ve V 0 e V 5 0 63V e So the capacitor is 63 charged at t RC The time to fully charge the capacitor will be infinite The capacitor will be 99 3 charged after five time constants When the switch in Figure 1 is at position B the capacitor will discharge its energy through the resistor When discharging a capacitor the voltage V and charge Q will decrease over time The voltage is characterized by the equation Vo t Vie UR L View If t RC 1 then the equation reduces to V t V e V 0 37V a So the capacitor is 37 discharged at t RC Since Q C V the amount of charge on capacitor while charging and discharging it is given by Charging Q t O 0 0 1 e 55 Discharging Q t Q e Q e For charging an initially uncharged capacitor or discharging an initially fully charged capacitor the circuit current varies as I gle E 56 Laboratory 6 Report Sheet RC Circuits Experimenters Course Date Objective The objective of this experiment is to use an RC circuit and the rate at which a capacitor charges and discharges namely the RC time constant to determine its capacitance Equipm
98. s it tends to be expensive and oftentimes delicate The equipment is tested and set up prior to the laboratory period but if you have any doubts about the functionality of the equipment or the way that it is set up it is important to ask the instructor prior to conducting the experiment If a piece of equipment is broken during an experiment promptly notify your instructor or laboratory assistant who will remove the broken apparatus to a designated place and replace it with functioning equipment Do not try to fix the equipment yourself All Laboratory Students Assistants Faculty and Staff must abide by the following safety rules when using the Physics or Physical Science Laboratories This list may be modified as deemed appropriate for specific situations Follow directions carefully when using any laboratory apparatus to prevent personal injury and damage to the apparatus The instructions on all warning signs including that given in writing on the walls and within the laboratory manuals as well as verbally given by faculty and other laboratory personnel must be read and obeyed Wear safety goggles provided by the department for the Absolute Zero laboratory especially when working near Liquid Nitrogen Each student MUST know the use and location of all first aid and emergency equipment in the laboratories and storage areas Each student must know the emergency telephone numbers to summon the fire fighters police emergency medical servic
99. s totally Set this switch to an easily observable range corresponding to the amplitude of the input signal 101 15 16 VARIABLE VAR PULLxSMAG Fine adjustment of sensitivity with a factor of greater than or equal to 1 2 5 of the indicated value For normal operation this knob must be turned all the way clockwise to the CAL position where the sensitivity is calibrated to the indicated value When this knob is pulled out KSMAG the amplifier sensitivity is multiplied by 5 19 20 VERTICAL POSITION Controls This knob is used to adjust the vertical position of the trace or spot 21 VERTICAL MODE Select Switch Selects the operation modes of the CH1 and CH2 amplifiers CH1 Operate the oscilloscope as a single channel instrument displaying the signal applied to CH1 alone CH2 Operate the oscilloscope as a single channel instrument displaying the signal applied to CH2 alone DUAL Operate the oscilloscope as a dual channel instrument displaying both signals applied respectively to CH1 and CH2 ADD The oscilloscope displays the algebraic sum CH1 CH2 or subtraction CH1 CH2 of the two signals The subtraction is in effect when the CH2 INV button 39 is pushed in 22 CH1 SIGNAL OUTPUT Delivers a voltage of approximately 20mV DIV from the CH1 signal to 50 ohm terminal for frequency counting Provides a sample of the signal applied to the CH1 connector 23 ALT CHOP Used in conjunction with 21 VERTICA
100. s used in our electricity labs are low it is best to be cautious when working with circuits make sure the power supply is off AND unplugged when assembling or disassembling a circuit Ensure the circuit is assembled properly before applying power to prevent damage to the equipment When using the ammeters and voltmeters in a circuit and the following is a good habit to get into in general when using failure to do so could result in damage to the meters e Be very careful in the use of the meters Start with the rheostat fully on if your circuit is connected to one e Use the largest scale on the meter then work your way down When varying the resistance of a circuit make sure that the resistance does not become small enough to burn out the meter Use caution with lasers do not point them at any person and do not look into the laser beam as blindness can result There is to be no eating or drinking in the laboratory professor included and no applying cosmetics combing of hair or other grooming activity 10 Open toed shoes are discouraged in the laboratory lab assistants and professor included as weights liquid nitrogen dry ice or other objects may accidentally drop on people s feet ordinary footwear provides a measure of protection from such instances Casual visitors to the laboratory are to be discouraged and MUST have permission from the Teaching Assistant Faculty Instructor of the section in question or Laboratory Sp
101. sei aiea test onsets ds seatceus ees aucepatuc oats S E E E EEE 9 1 Finding Absolute Zero iss iecasusics eeaasstesssantea vs leveguvasiebadaves gi eza sensed aadegs seca sdadad E aE tented os Eaa e a 12 2 o peed of Sound In Alasan a a a Get aces a a a e oa Eaa as 17 3 Electric Potential and Field Mapping ssesesssessssesssseessesssersserssseeesseesseesseesserssseessseesseessersseresseeessees 24 A Ones Taw anid IRESISUVIby wenden e a ncaa E Ea A E A E OREL 33 5 Series and Parallel RESIStOTS kisinin nia aa T RT aE IERE 40 ORE CUM ia at diet ate laa TE ENE A E A E E a te tlle saa ace ae ty 52 AENA EYA NAATA O KO ok IEEE EO E EEEE A EA AA T E EE 59 8 Magnetic Induction sinna eaa e aa La a EE e EE ATARA E E Ea oh da SEa aen ains 61 9 REC CUTS ce ae sl ea i ce Sia ore ne ace kel lod ga ae Nacht iat peel a ae an 67 10 Reflection and Refraction of Laser Light y i3icisccssscicssededasesvadancssdactisasdeaescagedaas sostadevabedeatasscbansnastone 81 LA Raser with Diffraction Grating ieat oret kie a n la a eaa a aea rtea SE eah 86 12 Convex and Concave Lenses osista ei asikie Ree Gece 88 Appendix A Computer Simulation Exercises s si c nied alge legend opening ds 91 Appendix B Introduction to the OscillOsCcope eesesscscsseceesseceessccecssececssccecscceessceeessceseseeeeeeeeess 93 Appendix C Experiments in Magnetic Force with PASCO s Basic Current Balance and Current Balance Accessory Four Experiments sesssesesssssessseessessse
102. sic linear analog components which when put together in various combinations exhibit behavior that is fundamental to much of analog electronics and thus have important applications They are commonly used as passive filters Two fundamental types of passive filters are the high pass filter and the low pass filter The high pass filter presents less attenuation to high frequency signals than low frequency signals by passing a signal through a capacitor or a path to ground through an inductor The low pass filter presents less attenuation to low frequency signals than high frequency signals by passing the signal through an inductor or by allowing a capacitor to provide a path to ground These are two types of electronic circuits that allow wanted frequencies to pass through while blocking unwanted ones If a capacitor C is connected to a voltage source V charge will acquire on the plates As the charge on the plates increases it becomes more difficult to add additional charge because of the increasing Coulomb force This continues until the voltage across the plates equals that of the voltage source At any time t the charge Q on the capacitor plates is given by Q CV The rate at which the capacitor charges and discharges is dependent on the capacitor and resistor in the circuit An important term in charging and discharging a capacitor is the RC time constant 54 Figure 1 Referring to the circuit shown in Figure 1 when the switch i
103. surements 45 Parallel resistors Click new 4 Create the schematic as shown in the figure 3 next page Click run and record your measurements Figure 3 Resistors in parallel Results Series Parallel Voltage Current Voltage Current Safety Reminder Caution Be very careful not to short circuit the power supply With too little resistance in a circuit the current can exceed 1 A The power supplies have a fuse that breaks the circuit if the current exceeds 1 A 46 Laboratory 5 Report Sheet Series and Parallel Resistors Experimenters Course Date Objective The objective of this experiment is to determine the equivalent circuit resistance of simple combinations of resistors in series and parallel Equipment Ammeter 0 0 5 A Voltmeter 0 10V Ohmmeter or multimeter Rheostats 44 Q or 177 Q or resistors Power supply 1 Connecting wires as needed WR Re Ww Procedure We will determine the equivalent resistance of the circuits below by four methods 1 Direct ohmmeter measurement of Reg 2 Theoretical Reg using individual ohmmeter measurements of R 3 Req from using ohm s law for circuit 4 Theoretical Req from individual Ohm s law measurements of R 1 Measure the resistance of each of the resistors and ammeters to be used below Note refer to the lab write up for schematics for each of the following circuits Series Circuit 2
104. tance and the power supply set to 0 or off and have the instructor check the circuit before activating 2 Turn up the DC volts of the power supply to 12V and adjust the rheostat until the current in the circuit as indicated by the ammeter is 0 5 A Record the meter values and the DC volts back to 0 as soon as possible to prevent heating and temperature change 3 Measure the length of the wire between the voltmeter connections and the diameter of the wire a Measure the voltage between each terminal to get five values remember to measure close to the spool and not at the terminals themselves b Record L in cm and A in cm so we can compare with published values more easily c The lengths are printed by each spool and the thickness of each wire is represented by the numbers 22 for one value and 28 for a thinner value d Thus if you carefully measure the thickness of 1 and 2 you can assume that the value of A for 1 is the same as that for 3 and 5 likewise for 2 and 4 e Thickness values are obtained by measuring as many consecutive turns as possible making sure they are one right next to another and not skewed count 36 the number N of turns and measure the length along N turns divide that value by N to get the diameter of a single turn f With the value for diameter D compute the cross section area A with the formula A 1D7 4 4 Find the percent error of the experimental values by comparing your values with the
105. tern you want and the diffraction pattern is horizontal on the white screen on the Aperture Bracket parallel to the ruled paper attached to the screen Tighten the thumbscrew on the Slit Accessory to hold it in place 4 Read off the position of the dark fringes in mm on either side of the central maximum For better accuracy a set of Vernier calipers can be used to measure the distances between the minima If you use the ruler to get the distance between the two subtract the smaller number from the larger and write this in the Data Table first space Repeat for the second and third sets of slits 5 Take each of the values you wrote in 4 and divide by two to get the distance of the minima from the central maxima and record these in the next column Using the parameters for a and on the Slit Accessory and laser respectively plug these values into the equation along with m 1 to solve for sin record in data table Repeat for m 2 and m 3 Refer to the Board to find out how to calculate the theoretical value for d 7 Repeat 2 to 5 for the multiple slit case you will only need to measure the distances and compare these to the corresponding distances for the single slit case and fill in that data table 8 For the first table compare your measured d s with your calculated ones using the difference formula D diff x100 cate A ziven given Finally in the back corner of the room are several lasers with transm
106. the induced voltage versus distance 65 What is the shape of the induced voltage in coil 2 versus distance Is this what you expected and why What did you observe about the emf values based upon the distance between the coils What is observed of the frequency in coil 2 How does it compare to the frequency in coil 1 What does this tell you Things to Consider 1 Do you think it is possible to measure the earth s magnetic field in a given direction by looking at the induced emf in a coil If so how would you construct the experiment and determine its value Can you use coil 2 to determine the presence of other signals in the vicinity How would you demonstrate this and which frequencies if any did you find How do you think the number of turns affects the outcome of the experiment 66 Pre Laboratory Exercise 9 RLC Circuits Name Course Date Consider the RLC circuit shown above with a peak voltage of 240 V f 60 Hz R 100 kQ L 0 5 mH C 200 uF Show your work 1 What is the impedance of the circuit 2 What is the value of the current read by the ammeter 3 What is the linear resonant frequency of the circuit 67 Laboratory 9 RLC Circuits Purpose The purpose of this experiment is to study currents and voltages in RLC circuits We will measure the response of the voltage across a resistor V as a function of a voltage applied at different frequencies Introduct
107. uF capacitor and a 3 50 MQ resistor form a series RC circuit what is the RC time constant Show work 5 Assume that a 10 0 uF capacitor a battery of emf 12 0 V and a voltmeter of 10 0 MQ impedence are used in a circuit such as that in Figure 2 The switch S is first closed and then the switch is opened What is the reading on the voltmeter 35 0 s after the switch is opened Show work 52 Figure 1 Power Supply E I C Capacitor Voltmeter Figure 2 53 Laboratory 6 RC Circuits Purpose The purpose of this activity is study currents and voltages in RC circuits We will use a Resistor and a Capacitor to study the capacitor s transient response as it is charged then discharged NOTE If you need to familiarize yourself with the oscilloscope before you start on this experiment work through the exercise in Appendix A designed to familiarize you with this instrument If you are doing this experiment using the computer and PASCO s DataStudio no such review is necessary a write up for this version of the lab is forthcoming Introduction and Theory A Resistive Capacitance or RC circuit is an electronic circuit that is driven by a voltage or current source such as a battery or power supply The simplest form of such a circuit is the First Order RC circuit consisting of one resistor and one capacitor Along with the inductor L the resistor and the capacitor make up three ba
108. unction Select one or more simulations from this list and do them varying the parameters and seeing how this varying affects the outcome of the experiment You could either choose an experiment that will not be done this semester or an experiment that has been done already In the latter case the initial conditions of the experiment can be modified to see how the results differ from that experienced in the classroom Your instructor may decide to use the simulation programs included in the Physics Learning Center instead of going online to the above site Internet problems may result in this as well Follow the directions given by the instructor and the simulation program s being used 92 Appendix B Introduction to the Oscilloscope By Dr Kevin Storr Purpose Introducing the Oscilloscope The purpose of this exercise is to learn how to operate an oscilloscope which includes observing and measuring fast and periodic electrical voltages Introduction amp Theory The cathode ray oscilloscope is an instrument which can be used to display the magnitudes of rapidly changing electric currents potentials or pulses as a function of time The information is displayed on a cathode ray tube CRT The CRT appears as a circular or rectangular window usually with a centimeter graph superimposed on it Of course a similar cathode ray tube is also an integral part of your television set The cathode ray tube consists essentially of an ele
109. up mass of the Magnet Assembly Record this value under Mass in Table 2 1 Subtract the mass that you measured with no current flowing from the mass that you measured with the current flowing Record this difference as the Force Turn the current off Remove the Current Loop and replace it with another Repeat steps 2 5 If you are using an electronic balance Place the magnet assembly on the pan of the balance With no current flowing press the TARE button bringing the reading to 0 00 grams Now turn the current on and adjust it to 2 0 amps Record the mass value in the Force column of Table 2 1 Turn the current off remove the Current Loop and replace it with another Repeat steps 2 4 Data Processing Plot a graph of Force vertical axis versus Length horizontal axis Analysis What is the nature of the relationship between these two variables What does this tell us about how changes in the length of a current carrying wire will affect the force that it feels when it is ina magnetic field Mass with I 0 Table 2 1 Data Length Mass Force Length Mass Force mm gram gram mm gram gram 109 Experiment 3 Force versus Magnetic Field Procedure Set up the apparatus as shown in Figure 2 1 Use the shortest length current loop If you are using a quadruple beam balance Mount a single magnet in the center of the ho
110. venient values In another setting R may be predetermined by the circuitry within which this circuit is found and which will use this last degree of freedom Other common uses of RLC circuits include the use of the circuit as an oscillator whereby the attenuation or damping factor is made as small as possible This can be adjusted by making the R be as small as possible for series circuits and as large as possible for parallel circuits Other uses also include making the circuit a voltage multiplier or a pulse discharge circuit An important property in RLC circuits is resonance which is the ability of the circuit to resonate at a specific frequency called the resonant frequency Resonance in the circuit happens because energy is stored in two different ways as an electric field as the capacitor is charged and as a magnetic field as the current flows through the inductor Energy can be transferred from one to the other and back again in an oscillatory mode much like the mass at the end of a spring oscillates back and forth between one extreme and the other The mathematics describing both are identical in form Whereas friction in the spring mass system will eventually bring the system to a halt the resistance in the RLC circuit will diminish the oscillation over time Like a vibrator that can keep the mass on a spring oscillating indefinitely the driving AC power source will keep the circuit resonating indefinitely 68 The resonant frequenc
111. y pass The magnetic flux is dependent on the strength of the magnetic field the size of the area through which they pass and the angle between the normal of the area and the magnetic field Recall that the electric flux through any closed surface is proportional to the electric charge enclosed by the surface There are no magnetic charges monopoles and the magnetic flux through any closed surface is zero However a changing magnetic flux will produce an emf in a conductor and cause a current to flow Magnetic flux through a surface is defined as BAcos where B is the magnetic field in tesla A the area in m and the angle between the area normal and the magnetic field When 0 is 90 the magnetic field is in the plane of the surface and 0 When 0 or 180 the magnetic field is perpendicular to the surface and is a maximum value BA 61 Faraday s law states a changing magnetic field induces an electric field this is summarized in the f A i following equation ere where e is the electromotive force and is the magnetic flux It t states if we have a magnetic flux which changes in time it induces an emf If that emf is induced in a material capable of carrying a current a current will result The sense of the current will be such that it produces a magnetic field that opposes the changing magnetic flux This is Lenz s law The induced current in a loop is in the direction that creates a magnetic fi
112. y is defined as the frequency at which the impedance of the circuit is at a minimum In the series LRC circuit that we will be studying the impedance reaches a minimum when resonance is achieved in parallel LRC circuits this happens when the impedance reaches a maximum The resonant frequency is reached because the inductor and capacitor are equal but of opposite sign so they cancel out The AC current of a RLC circuit connected in series depends on the voltage and impedance Z Impedance is the AC circuit equivalent of resistance This describes not only the amplitude of voltages and currents but also the relative phases The impedance is defined mathematically as z X X R j 1 Where the inductive reactance is X Lthe capacitance reactance is X E and R is the resistance and the angular frequency is 2af where f is the linear frequency The current will have a maximum value at resonance when X L7 X g this condition defines the resonant 1 er me frequency at For this condition the impedance Z R and has a minimum value res VLC which results in the current having a maximum value Note This lab has several variations which are included below The standard report sheet with its procedure is also included The professor may decide to do one or the other or a combination of both In addition an electronic workbench activity is added Suggested Procedure 1 Set up the circuit as shown be

Physics 2121 Lab Manual

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