Unit 3: Students Absolutely Must Learn…
Contents
1. Veource t Vmaxsin wt o A where Vmax 5 Volts w 2x 1 000 Hz Use this sinusoidal voltage to power a 1 000 Q resistor Use the oscilloscope to measure the voltage drop across the resistor set up as shown in the picture below Vsource t VuaxSin wt 9 AN where Vmax 5 Volts w 2x 1 000 Hz 2 B 1 What should the voltage drop across the resistor be according to conservation of energy Be sure your measurement with the oscilloscope indicates this 43 Now switch to a 10 Q resistor and examine the voltage drop across it Theoretically this smaller resistor should still have the same 5 Volt difference amplitude as the 1 000 Q resistor However you should notice the voltage amplitude decrease This is a result of the function generator output changing The smaller resistor will allow a greater current to flow through the circuit but the function generator has a maximum current that it is able to produce Therefore once the resistance becomes too low the function generator cannot output the full 5 volts 2 B 2 Imagine that you are about to use the function generator to power a circuit Explain why you should measure the amplitude of the source voltage coming from the function generator after you have hooked up the function generator to your circuit Many students get bad data because they forget about this subtle issue 2 B 3 em P Use the equation 7 E in with the 10 Q resistor to find t2. 2 C 6 Determine the amplitudes of the voltage differences across each resistor and explain why this makes sense Using the same middle ground set up as in the last problem measure the changing voltage across both resistors in X Y mode so that one of the resistor voltages is plotted on the x axis and the voltage of the other resistor is plotted on the y axis You should see an ellipse edge on i e a diagonal line In the prelab you found an elliptical x y graph because the voltages being plotted were out of phase However in today s lab we don t have any components that cause phase shifts i e capacitors or inductors Since both voltages are oscillating in phase they will both reach zero simultaneously Thus they will trace a diagonal line that some experimentalists simply consider an ellipse viewed on edge 2 C 7 How does the height and width of the ellipse in your x y measurement relate to the voltage amplitudes across each resistor 48 In Lab Section 3 non ohmic diodes A diode is a one way circuit component If a potential difference is applied the wrong way across a diode it will act as an infinite resistance and not conduct electricity If a voltage is applied correctly across a diode and above a minimum value the diode will act with almost zero resistance and allow the current to flow through it This strange behavior is entirely quantum mechanical and non Ohmic This turn on effect is related to
3. in your lab report so work through it now to make sure you understand Write an explanation down for every step Explain using either physics concepts or mathematical operations Jod I T L S R R ag R R R R Therefore R parallel 11 Subsection 0 D Solving compound circuits is a very important skill Here is an example where you must solve for the total current which is the current through the battery Ipattery the total resistance Rio as well as the voltages across and currents through each of the components R 4 Q R 1Q V 10V IBattery The strategy is to pretend that the two series resistors are equivalent to a single resistor R2 Ra 10V 10V R lt gt First collapse the two series components R R R 5 Q Since this is actually the total resistance of the circuit assuming an ideal battery which has zero internal resistance you may use Ohm s law to find the total current Ipay i 2 A A Since charge cannot pile up anywhere in a circuit this is also the same current as in Ri and Rz J I 2 A You can now find the voltage across Ri V RJ 2 V and Rz V R I 8 V Due to the conservation of energy you expect the voltages across the components to add to the total supplied by the battery and indeed 248 10 12 As more components are added to the circuit the problem solving becomes more complex Here you must solve for the total current Igatte
4. the reason for your answer 0 B 2 Label the voltage difference across each resistor as V4 and V Write an equation relating V to V and V Here you must use the idea that the sum of all voltage differences in a circuit must be zero or else one could extract an infinite amount of energy from the electrons whirling around the loop 0 B 3 Now use Ohm s law in your previous to substitute R and I for Vi and R and I for V2 At this point your equation should read V R L R 0 B 4 Now use your answer from 0 B 1 by substituting for and Z since 7 there is no reason to differentiate between the current in the two resistors so just write I Distribute the I from the addition on the right hand side of the equation to get R R Explain why this tells you that two resistors in series have an equivalent resistance of R R 0 B 5 If V 23 V R 4 Q and R 6 Q find the current through the resistors 0 B 6 If V 3 V R 4 Q and R 6 Q find the current through the battery remember charge can never pile up anywhere in a circuit 10 Subsection 0 C R R equivalent Now examine two resistors in parallel We would like to be able to treat them as a single equivalent resistor to make examining the total behavior of the circuit easier The derivation is given below without explanations 0 C 1 You will need to provide the derivation with explanations for each step
5. 1 If the temperature is low so that each electron in the valence band of the semiconductor has an average kinetic energy much less than the band gap energy explain whether the semiconductor acts as a conductor or insulator 1 2 Imagine that an external voltage source is applied across the semiconductor so that each valence electron has more kinetic energy Approximately what must the applied external voltage be in order for the semiconductor to transition from an insulator to a conductor Hint energy equals charge times electric potential Diodes are layered semiconductors and in a simple circuit act as one way components Light emitting diodes LEDs have a myriad of practical uses The photons emitted by an LED each have energy roughly equal to the band gap energy of the semiconductor Laser diodes are conceptually similar to LEDs and have led directly to the digitized age of music More and more electrical engineering programs requiring their majors to gain a firm understanding of quantum mechanics Not a question 40 In Lab Section 2 time dependent voltage on the oscilloscope Subsection A The following picture shows the digital oscilloscope and labels its most common features screen menu calcs amp info menu buttons each channel Close up amp split apart view of digital oscilloscope autoset cursor wi control f measure cursor triggering control usual channel controls You now need to
6. Requivatent 9V latior First find the total equivalent resistance This must be done in steps First collapse the first two parallel components amp Os Then collapse this with Rs R 29g 245 3 1 1 n i Am R R Finally collapse these with the remaining Ra Ropective R R3 Ta With the total resistance you may use Ohm s law to find the total current y Battery NN ES nne This is also the same current as in Ra 7 Amps You can now 50 effective find the voltage across R4 V R 1 Volts Now note that R R2 and Rs are in parallel so that Vi V2 V3 conservation of energy in loops Subtract V4 from the total voltage to find the voltage across each parallel component V V V 9g 8 L Volts 25 23 Now you can easily find the current in each component J Ls Z uns I L ET npe R 25 R 50 and J HI LOT np x 75 22 2 C 1 Calculate the total circuit resistance and total circuit current Then calculate the current through the 3 ohm resistor 3V 2 C 2 Calculate the total circuit resistance and total circuit current Then calculate the current through the 3 ohm resistor 3V 23 2 C 3 Calculate the total circuit resistance and total circuit current Then calculate the current through the 3 ohm resistor 3V 1Q 2 3Q 19 22 2 C 4 Calculate the total circuit resistance and total circuit current Then calculate the current through the 3 ohm res
7. Unit 3 Students Absolutely Must Learn Weekly Activity 5 Vulture Iguana Rabbit How resistance R is defined whether or not a component is ohmic How R V and I are related in ohmic devices How to find equivalent resistances in series and parallel How to find equivalent resistances of complex compound circuits How to use ohms law to find voltages and currents for all parts of a circuit How to make an ammeter measurement Weekly Activity 6 Oscilloscope How to relate the mathematics of the sine function to the appearance on the oscilloscope screen of a sinusoidally oscillating voltage The basic concept of how a semiconducting component works especially relating to its band gap energy or turn on voltage How to use an oscilloscope to measure voltage How to set up middle ground and bottom ground simultaneous voltage measurements Unit 3 Grading Guidelines Staple the lab report then graphs and finally worksheets together Please put your worksheets in order Turn in your work to your TA at the beginning of the next lab meeting following the completion of the unit Unit Lab Report 50 graded out of 25 points Write a separate section using the section titles below be sure to label these sections in your report In order to save time you may add diagrams and equations by hand to your final printout However images text or equations plagiarized from the internet are not allowed Remember to write your report alone as c
8. age between red 1 and ground will tell you the potential difference across both resistors while the voltage between red 2 and ground will tell you the voltage across the 200 Q resistor red 1 100 Q 200 Q 2 C 1 What must you do mathematically to find the voltage across the 100 resistor 2 C 2 Are the two oscillating voltages across the resistors in phase with each other 2 C 3 Determine the amplitudes of the voltage differences across each resistor and explain why this makes sense 46 Now use the oscilloscope to measure the voltage across each resistor simultaneously on both channels by setting up a middle ground set up as shown in the figure below Note that the middle ground measurement requires that the function generator NOT be grounded use a 3 to 2 prong plug adapter on the function generator The voltage between red 1 and ground will tell you the potential difference across the 100 Q resistor while the voltage between red 2 and ground will tell you the inverted voltage across the 200 Q resistor The voltage reading is inverted because the order of the positive and negative leads of the second channel are reversed the same thing would happen with a simple DMM when you switch the leads red 1 100 Q 200 Q 2 C 4 What must you do mathematically to find the total voltage drop across both resistors 2 C 5 Are the two oscillating voltages across the resistors in phase with each other 47
9. ave a frequency of 60 Hz but V has an amplitude of 6 V while V has an amplitude of 12 V Furthermore V lags behind V out of phase by 90 Without making a data table sketch what would appear on the oscilloscope Feel free to use a graphing calculator with the functions V f 6sin 2z 60 f and V r 12sin 27 60 etj Be sure to label your axes and choose appropriate time and voltage units per division for your graph a i E il uw I E iili ig He E E 0 6 Finally imagine taking the two alternating voltage sources from the previous problem but now graph V t on the x axis and V t on the y axis In oscilloscope terminology this is called an XY plot Thus we are graphing V vs V4 Note this is a voltage vs voltage graph NOT a voltage vs time graph Make a data table using some points of common time provided below and the formulas from the previous sections Use this table to graph V vs V1 Be sure to label your axes and choose appropriate voltage units per division for your graph t sec V Volts V Volts This page intentionally left blank 38 In Lab Section 1 semiconductors and quantum mechanics Generic Plot of Energy Bands for Semiconductor Energy eV conduction band empty AE is called Band Gap Energy valence band filled with electrons Momentum The above graph shows the energy bands for a generic semiconductor which must be calculated
10. b is to figure out the answer using these prompts as your problem solving model In the event that you should run out of time you may not discover the correct answer but you should make an attempt at each prompt Grades are based on honest effort Your open ended solution should probably include some of the following items sketches of circuit diagrams tables of data calculations recorded observations random ideas etc 5 1 hypothesizing planning 5 2 observations data 5 3 calculations conclusion the physics 241 laboratory TA have examined this student s Weekly Activity pages and found them to be thoroughly completed TA signature 54 Post Lab oscilloscope You must complete this post lab section after you attend your lab You may work on this post lab during lab if you have time and have finished all the other lab sections XA Which would be the best choice for time steps At when graphing V t 28sin 5 000 7 volts with time measured in s in order to observe 3 10 oscillations on the graph below V t 5 55 red 1 red 1 A red 2 inverted middle ground 200 Q 200 Q Most oscilloscopes have two channels so that two simultaneous voltage measurements may be made Since both share a common ground only one of their grounds needs to be connected to the circuit This can be done is two ways a middle ground configuration or a bottom ground configuration Explain why one co
11. empts resulted in failure explain what went wrong and what you would do differently in the future You must write using sentences amp paragraphs bulleted lists are unacceptable Graphs 4 points attach to typed report Graphs must be neatly hand drawn during lab and placed directly after your typed discussion before your quizzes and selected worksheets Your graphs must fill the entire page requires planning ahead and must include a descriptive title labeled axes numeric tic marks on the axes unit labels on the axes and if the graph is linear the line of best fit written directly onto the graph Thoroughly Completed Activity Worksheets 30 graded out of 15 points e Week 5 In Class 7 points Pages assigned to turn in TA signature page Post lab pages e Week 6 In Class 8 points Pages assigned to turn in TA signature page Post lab pages The above lab report and worksheets account for 80 of your unit grade The other 20 comes from your weekly quizzes each worth 10 These will be entered into D2L separately Weekly Activity 5 Vulture Iguana Rabbit Pre Lab You must complete this pre lab section before you attend your lab to prepare for a short quiz Be sure to complete all pages of the pre lab STOP PRELAB Continue until you see the stop pre lab picture e Subsection 0 A The resistance of a circuit is defined to be the amount of voltage applied to the circuit divided V by the total current th
12. explained Any other specific TA requests Selected In Class Section 6 points 3 5 paragraphs 1 page This week s selection is Weekly Activity 6 In Lab Section 3 Write a mini report for this section of the lab manual Describe what you did succinctly and then what you found accurately Then explain what the result means and how it relates to some of the concepts in the previous section You must write using sentences amp paragraphs bulleted lists are unacceptable o Procedure Do not provide a lot of specific details but rather you should summarize the procedure so that a student who took the course a few years ago would understand what you did o Results Do not bother to rewrite tables of data but rather refer to the page number on which it is found State any measured values slopes of ilnes of best fit etc Do not interpret your results save any interpretation for the discussion o Discussion Analyze and interpret the results you observed measured in terms of some of the concepts and equations of this unit It is all right to sound repetitive with other parts of the report Open Ended Creative Design 6 points 3 5 paragraph 1 page Choose one of the open ended experiments from the two weekly activities to write about Describe your experimental goal and the question you were trying to answer Explain the ideas you came up with and what you tried If your attempts were successful explain your results If your att
13. he maximum mplitude current amplitude J amplitudemax that the function generator is able to produce 44 Subsection C You may use the oscilloscope to measure the voltages of two circuit components separately using the oscilloscopes two separate channels The two oscilloscope channels each have a ground black lead and both grounds are actually connected inside the oscilloscope so that only one ground needs to be connected to the circuit A common mistake is for students to try and sandwich each component with both channel leads WRONG red 1 black 1 100 2000 black 2 red 2 The problem with using both channel grounds is that 1 it is not necessary since they connected internally and 2 if they end up being connected to different parts of the circuit they short the circuit out because they are connected internally Sometimes students use an external wire to connect both black leads of the oscilloscope channels to remind themselves of this so they don t end up making mistakes on their lab practicals Never use both channel grounds Only use one of them either will do 45 Set up the function generator to output a 200 Hz sine wave with a 3 Volt amplitude through a 100 Q and a 200 Q resistor in series see figure below Use the two oscilloscope channels to measure the voltage across each resistor simultaneously on both channels by setting up a bottom ground set up as shown in the figure below The volt
14. ickel chromium of various thickness Nichrome wire has a very high resistance and is often used in simple heating elements Imagine you work for a company that produces resistive wire You need to determine some basic technical specifications for the resistive wire for use in your sales catalog Reporting the total resistance is useless since this depends on how thick and long a particular wire is Instead you should report resistivity p with units of Q m which is a microscopic description of resistance This will allow an engineer designing a coffee maker the ability to calculate the size and shape of the Nichrome heating element that they need to order from your company The total resistance of a wire increases linearly with the length of the wire Roc L However the total resistance of a wire is inversely proportional to the cross sectional area of a wire R es This is because increasing the thickness of the wire gives the electrons more surface to flow through so that they encounter less electrical friction When someone knows the proportionalities of a variable they can write an equation for that f L ee variable with an unknown constant R E Here the resistivity p is a constant of proportionality relating the total resistance of a wire to its length and area Find the resistivity of Nichrome wire V a lt P ROSS SECTION L You are allowed to cheat by talking to other groups for ideas but are not allowed to cheat b
15. istor 3V 2Q 2 C 5 Would you have predicted that the total current for the third circuit would be so different from the total current in the fourth circuit Explain why the addition of the single 1 Q resistor in the fourth circuit increases the total current by almost 300 Your answer and explanation 24 In Lab Section 3 the internal resistance of a DMM Your DMM has a very large internal resistance Sometimes it is important to know this value because if you try to measure circuits with comparably large resistances the DMM begins to carry an appreciable part of the circuit current throwing off measurements For example in the following picture a DMM is used to measure the voltage across a resistor Consider what happens if the internal resistance of the DMM is near to that of Ri It behaves like any resistor by letting current flow through it Since the resistance of R is so large more current than is supposed to flows through the DMM Since DMM actually measures voltage by determining the current flowing through it a false reading is obtained We can find the internal resistance of the DMM by deriving a useful formula relating Romm to other variables and then measuring the other variables experimentally Theoretically examine the circuit with R placed in series with the DMM You won t be asked to set up the circuit and make measurements until a later problem 34 Predict the total resistance of this circui
16. loscope You may simply uninvert this on your graph paper 51 This page intentionally left blank 52 In Lab Section 4 authentic assessment 4 1 Quickly set up a working circuit of a resistor powered by a sinusoidal voltage at 100 Hz and measure the current amplitude through the resistor Actually you can only measure voltage with an oscilloscope so you must do this by measuring the voltage drop amplitude across the resistor and applying a special amplitude amplitude version of Ohm s law ES Actually Ohm s law is valid amplitude for any point in time so it must hold at the instant when the current and voltage reach their maximums amplitudes Show your results to a student in a different group Yes have seen this student use the voltage measurements of an oscilloscope to obtain the amplitude of the current through a resistor In other words they know how to find the voltage amplitude and divide by the resistance Student Signature 53 In Lab Section 5 open ended creative design Prove that a light bulb is non ohmic because of heating affects by examining the correct graph on the oscilloscope You are allowed to cheat by talking to other groups for ideas but are not allowed to cheat by just stating an answer you may already know looking it up online or asking your TA Below you are given three prompts hypothesizing planning observations data calculations conclusion Your jo
17. m resistor like a wire you will NOT obtain a 1 500 000 amp current As the battery tries to supply a large current it will heat up and its internal resistance will grow thereby lowering the voltage supplied to the resistor until only a small voltage is actually applied to the resistor 0 A 5 If your 12 volt car battery dies unexpectedly why can t you substitute your car battery with eight 1 5 V batteries 8 x 1 5 V 12 V in series to get home Answer the questions about each of the following graphs 0 A 6 Does the below graph describe an ohmic resistor What does the slope of this graph represent AV applied Tinrough 0 A 7 Does this graph describe an ohmic resistor R Through 0 A 8 Does this graph describe an ohmic resistor Through AV acpioa 0 A 9 Does this graph describe an ohmic resistor I AM applied 0 A 10 Does this graph describe an ohmic resistor R AV applied Subsection 0 B When two resistors are put into series it is often useful to treat them as a single composite resistor and to find the equivalent resistance of this single resistor The formula for this is Raven R R You will learn to derive this by answering the following questions using the below picture equivalent Jem us pr mm 0 B 1 Label the current through each resistor as I and I Because the resistors are in series how are these two currents related think marbles in a hose What is
18. ne you have a 1 5 V battery and you measure the voltage every second for 5 s Make a data table to describe this t vs V Then use the data table to make a graph of what you would see on the oscilloscope screen Your oscilloscope allows you to control the size of the tick marks on its screen FOR THIS PROBLEM ONLY you are provided a choice of axis settings and selection of origin For all other problems you will need to select the appropriate axis settings yourself Connect your data points on your graph to demonstrate what the oscilloscope would really show Hint this is about the simplest graph in the world i e a straight line t V Voltage 0 5 volts per div Time 1 second per div fT ttt ty ae rui jit tt TERRAE ECC 34 0 4 Now imagine you have a 6 V sinusoidal power supply with a frequency of f 60 Hz What is Vmax and Vmin for this voltage and What is the period of one oscillation Mathematically this voltage is described as V r 6sin 2z 60 where 27 60 is the angular frequency Fill in the data table below by plugging the times into the sinusoidal voltage formula calculator in radian mode Then make a graph on the oscilloscope Be sure to label your axes and choose your units per division on the time axis wisely so that all your data fits on the screen FK ILIITLIITLIIN ekda EE Id feb HARE Volts 0 5 Now imagine you have two sinusoidal voltage signals Both h
19. nfiguration is better for measuring the voltages of two separate components while another configuration is better for measuring the voltage of one component and the total applied voltage X 3 The band gap energy of pure silicon is approximately 1 eV electron volt or in SI units 1 6x10 joules so 1 eV 1 6x10 J Using the formula that relates electrical potential energy to electric potential U V where the band gap energy is substituted for U and the charge of an electron e 1 6x10 C is substituted for q you can find the voltage that would need to be applied to turn on pure silicon and make it a conductor Your answer should be 1 volt By checking that 1 volt is correct you should now be able to explain why electrical engineers sometimes use the strange energy unit of electron volt rather than the SI energy unit joule Explain why the energy unit eV is useful 56
20. o work inward then back outward on these kinds of problems 14 0 D 1 The following compound circuit shows a 10 V battery discharging through two parallel 2 ohm resistors and two 8 ohm resistors in parallel The two parallel pairs of resistors are themselves in series You need to find all the unknown component voltages and currents as well as the total circuit resistance and current You may assume the battery is ideal has no internal resistance The answers are given so that you can check your work Hint treat each parallel set of resistors as a single equivalent resistor R 2 Q L V3 Riotal 5 ohms otal 2 amps V V 8 volts I 1 1 amp 10V R7 80 V V 2 volts Tpattery L V L I 1 amp 15 This page intentionally left blank 16 In Lab Section 1 experimentally determining resistance 1 1 Make a sketch of the small board of resistors provided to you and use your DMM to measure the resistance of each with as much accuracy as possible Label the values on your sketch There is never any reason to trust the values written on the resistors or the color codes The picture below is provided to remind you that to measure current you must divert the charges flowing in the circuit through the DMM so that it may count them as pass through Measuring the current through a light bulb DMM in series Do not apply such a large voltage that the resistor becomes very ho
21. ollaborating with a lab partner may make you both guilty of plagiarism Pay close attention to your teacher for any changes to these guidelines e Title 0 points A catchy title worth zero points so make it fun e Concepts amp Equations 9 points One small paragraph for each important concept as many paragraphs as it takes 2 pages Go over the lab activities and make a list of all the different concepts and equations that were covered Then simply one at a time write a short paragraph explaining them You must write using sentences amp paragraphs bulleted lists are unacceptable Some example concepts for this unit report include but are not limited to What is the definition of resistance Explain what it means for the component of a circuit to be Ohmic Derive the series addition equation Rra R R 1 Derive the parallel addition equation Rot TT R R Derive the equation used to find Romm Row Yow pg V Vomm Explain the problem solving strategy to deal with circuits utilizing many resistors in series and in parallel How why do you measure time dependent voltage How why do you measure two time dependent voltages How why do you measure two voltages in an XY plot How do you use VOLTS DIV and SECONDS DIV to get numerical data from the oscilloscope screen How do you use all the other various knobs and levers on the oscilloscope Any other equations that were used in the activities will need
22. ow are they related Without using equations explain why you expect the current to act this way c Compare the magnitude of the voltages between point pairs a b b c and a c How are they related Without using equations explain why you expect the voltage to act this way d If these resistors are two light bulbs explain which light bulb is brighter 30 X 2 Resistors in Parallel 0 oO 200 Q V a How does the total resistance of the circuit compare to the resistance of each individual resistor smaller larger the same Without equations explain why you expect the total resistance should be this way b Compare the currents at points a b c d e and f in the circuit How are they related Without using equations explain why you expect the current to act this way c Compare the magnitude of the voltages between point pairs a b c d and e f How are they related Without using equations explain why you expect the voltage to act this way d If these resistors are two light bulbs explain which light bulb is brighter 31 This page intentionally left blank 32 Weekly Activity 6 Oscilloscope Pre Lab You must complete this pre lab section before you attend your lab to prepare for a short quiz Be sure to complete all pages of the pre lab STOP PRELAB Continue until you see the stop pre lab picture e Before actually using the oscilloscope you need to be able to understand and predict wha
23. practice using the digital oscilloscope so that you are prepared to make measurements with it Keep in mind that the oscilloscope is simply a tool that allows you to analyze the details of a rapidly changing voltage With that in mind you will now practice the more common measurements that are made as well as their uses Your TA will most likely have demonstrated how to use it at the beginning of lab but each student will forget different features at the beginning stages so work together and ask lots of questions 41 2 A 1 Hook the two output leads of your function generator to the two leads of channel 1 of your oscilloscope Use the oscilloscope to examine the voltage vs time graphs of many different sine waves square waves and saw tooth waves created by the function generator oscillating voltage supply Be sure to experiment with all sorts of frequencies voltage amplitudes and DC offsets Practice making the voltage functions fit nicely on the oscilloscope screen Take the time to twiddle every knob and switch Once you feel comfortable with your understanding of each operational control of the oscilloscope and function generator write a short statement explaining what each control does But don t write a user s manual 42 Subsection B Use the function generator to create a 5 volt sine wave with 1 000 Hz frequency Use the oscilloscope as shown in the picture below to set the function generator amplitude correctly at 5 0 Volts
24. ree resistors in parallel SI units Also provide a small sketch of the simplified circuit 2 A 2 Now use the formula for the equivalent resistance of resistors in series to predict the total resistance of this circuit SI units 19 2 A 3 Now set up the circuit and test your prediction by simply using the DMM as an Ohmmeter Redo 2 1 and 2 2 until you are sure you are calculating your prediction correctly and or making the measurement correctly Subsection 2 B 100 2 2000 100 Q 10 Q 2 B 1 Power the circuit from the previous problem Be careful not to use too large of a voltage or the resistors will become very hot Measure the voltage drop across each of the resistors in parallel What do you find and why 20 2 B 2 Measure the voltage across the 10 Q resistor Does this value make sense i e does it equal the total applied voltage minus the voltage across the parallel components e 2 B 3 Measure the total circuit current How must the currents in each of the resistors above compare to this Measure each of the currents in the resistors and check that this is so Don t cut corners here or you will not do well on the lab practical 21 Subsection 2 C Solving compound circuits made from ohmic components is a very important skill Here is an example where you must solve for total current Igattery total resistance Requivalent aS Well as the voltages and currents in each of the components R 4 Q
25. rough the circuit R When someone speaks of the total resistance of a component of a circuit they mean the voltage drop across the component AV rop across component component I divided by the current flowing through the component R through component 0 A 1 The SI unit of resistance is ohms denoted by the Greek capital letter Omega Q Express the SI unit of ohms in terms of other electricity SI units If a circuit component has a high resistance it will require a larger applied voltage to obtain a desired current trough the component Note that even though a 12 V car battery can deliver a great deal of power it will not light a household light bulb which has a high resistance designed for the much higher 120 V household voltages 0 A 2 If you apply a voltage difference across a light bulb but only get a trickle of current through the light bulb what can you qualitatively say about the light bulb s resistance Justify this using the definition of resistance Imagine you are in the desert and there is a vulture flying in the sky and a rabbit and an iguana walking on the ground The rabbit sees the vulture flying over the iguana This is a pneumonic Vulture Iguana device to remember the definition of resistance R p Rabbit sees 0 A 3 What would the iguana see What would the vulture see Write two new equations relating V and R based upon this pneumonic device This is merely a wa
26. ry the total resistance Rtotai as well as the voltages across and currents through each of the components R34 Q R 2Q L VA First find the total equivalent resistance This must be done in steps 4 Q 9V TQ 40 9V Ra Re 9V 13 e First collapse the first two parallel components R 2 Q Then collapse R R 14 the two series components R R R us Q Since this is actually the total resistance of the circuit assuming an ideal battery which has zero internal resistance V Battery 27 Battery R 14 you may use Ohm s law to find the total current A e Since charge cannot pile up anywhere in a circuit this is also the same current as in Rs I A You can now find the voltage across Rs V R V e Now note that R and R3 are in parallel so that V V2 remember conservation of energy in circuit loops Subtract V3 from the total voltage to find the voltage across these 54 9 parallel resistors V V oe V Now you can easily find the current in V 9 V each component J A and J rx m A Check your parallel currents 1 2 9 9 721 ON as they must add up to the total 7 I z vi T A which is the total current coming into the parallel components Also note that since R3 has twice the resistance of R only half as much current flows through that resistor The logic is beautiful but it takes a good amount of practice to learn how t
27. t dangerous and non ohmic 1 2 Experimentally verify that the 1 000 Q resistor on your resistor board is ohmic at room temperature Do this by gathering voltage current data and making the appropriate graph Your graph of your data should quite nicely show the linear behavior of your ohmic resistor The correct choice of V vs I or I vs V should give your resistance as the slope and thereby check its experimentally measured resistance see how close you got with your DMM redo if bad write data here and plot graph on separate graph paper 1 3 Experimentally verify that the 100 Q resistor and the 200 Q resistor in series produce an equivalent resistance of 300 Q by taking voltage current data and making the appropriate graph Your voltage data should be gathered from across both resistors simultaneously since you want to treat them as a single resistor and find their equivalent resistance Remember that the current is the same through both resistors Do not apply such a large voltage that the resistor becomes very hot dangerous and non ohmic write data here and plot graph on separate graph paper 18 In Lab Section 2 compound circuits Subsection 2 A 100 Q 2000100 2 10 Q 2 A 1 The circuit shown above has 3 resistors in parallel which together are in series with another resistor Extend your equation for the parallel resistance of two resistors to find the equivalent resistance of th
28. t from the two component resistances 25 3 2 Calculate the total current I in the circuit in terms of V Ri and Romm 3 3 Since the total current is also the current through Rpyy you may also calculate in terms of Romm and Vomm 3 4 Equate I in your previous two answers in order to find an equation relating V Ri Romm and Vomm 3 5 i V Rearrange your previous answer in order to obtain Rpm A R UU DMM 3 6 With the aid of your derived formula given in 3 5 use your DMM and the 1 MQ resistor to find the internal resistance of your DMM 26 In Lab Section 4 authentic assessment Set up a working circuit that simultaneously uses three resistors not all in series and measure the current through each resistor separately using an ammeter Be sure not to apply too large of a voltage Sketch your circuit and label the resistances and measured currents of each resistor 4 1 Show a student in a different group that you can successfully measure the current through a resistor using an ammeter Once you are successful have them sign below Note if someone is stuck please give them advice Yes have seen this successfully use make an ammeter measurement They have not forgotten the major difference between measuring voltage and measuring current with a DMM Student Signature 27 In Lab Section 5 open ended creative design At each lab station is a long board with Nichrome wire n
29. t will appear on the oscilloscope screen An oscilloscope is a device that measures voltage differences over time It can be used to study rapidly oscillating voltages For example the voltage supplied by a wall outlet oscillates at the incredibly slow rate of 60 Hz Hertz Hz is the SI unit for linear frequency representing the number of oscillations per second However the oscilloscope can easily measure an oscillation of 1MHz or more Most DMMs indicate that they can measure an oscillating voltage However a DMM can only make average measurements of sinusoidal 60 Hz voltages In other words a DMM is only useful for alternating current measurements AC on household circuits not radios or other electronics 0 1 What is the period T of one oscillation for a linear frequency f 5 MHz sinusoidal oscillating voltage What is the angular frequency Remember T 1 f with SI units s and 2zf with SI units 1 s An oscilloscope is needed to examine voltages that change in time Mathematically a voltage that oscillates sinusoidally can be written as a time dependent function with time measured in seconds s V t 2 6sin 2z 60 t volts where f 60 Hz 277 60 1 s and Vamplitude 6 volts 0 2 For the sinusoidal voltage V r 8 21sin 255 r volts find f T and Vamplituae all in SI units 33 The simplest way to use an oscilloscope is measuring a constant voltage which even a DMM can do 0 3 Imagi
30. t you cannot directly measure the current through the LED with the oscilloscope Therefore answer the following questions first in order to learn how to construct the liep VS Vapplied graph ep responding to different V a possible non Ohmic graph AV applied many various applied V s 3 3 In this circuit how is the current through the LED related to the current through the resistor 3 4 Which component of your circuit is known to be ohmic 50 3 5 While the circuit is in operation if you know the voltage across the resistor and its resistance what can you find Your answers to the previous questions should help you understand that you need to measure the voltage across the resistor in order to find the current through the resistor Therefore you need to create the Vg vs Vapplied graph and turn it into the liep VS Vappiied graph simply by dividing the y values by the resistors resistance AVR lleb a non Ohmic graph R AV applied AV applied many various many various applied V s applied V s VruRN ON 3 6 Make measurements to obtain the first graph and use it to calculate and create the second graph Finally your measurements allow you to experimentally obtain the quantum mechanical property of the material the turn on voltage so record this value below Note that due to the direction the diode is soldered into the circuit some students may have inverted readings on the oscil
31. the band gap energy of the semiconducting materials the diode is made of Note that vacuum tubes perform a similar function to diodes and are not quantum mechanical in nature Create the powered diode circuit with a light emitting diode LED in series with a resistor On many diode boards the diode is already soldered in series with a 330 Q resistor Start using a very low source frequency so that you can see the LED blinking as current passes through the LED half the time Do not forget the resistor as it protects the diode from being destroyed by a large current Then set up your oscilloscope in the bottom ground set up to measure the voltage across the resistor on the y axis and the applied voltage on the x axis red1 Vamp 3 V CV ground Since the voltage source is oscillating some of the time it is in the correct direction to turn on the diode so that current can flow and some of the time is in the opposite direction so that no current flows 3 1 When current flows through the circuit which component has zero voltage drop across it and why 49 3 2 When current not flowing through the circuit which component has zero voltage drop across it and why Experimentally determine if the diode is Ohmic by constructing its current versus applied voltage graph should look something like example figure below You may want to increase the source frequency so that the oscilloscope trace makes a solid line Note tha
32. using quantum mechanics This graph shows a plot of possible energy states for electrons inside semiconducting material such as one would find in a computer chip Though an in depth discussion of this advanced topic cannot be given here the most essential points can be provided The lower energy band of a semiconductor is completely full of electrons It is out of room so to speak Electrons in this low energy band cannot accept extra energy unless it is sufficiently large enough to move the electron into the next energy band called a conduction band Thus a very cold semiconductor cannot conduct electricity because the electrons are stuck in the valence band But if enough voltage is applied to a semiconductor the electrons can be given enough energy to escape the valence band and move into the conduction band And so you may now guess at how semiconductors provide us a way to create digital electronics that is electronics that is either on or off 1 or 0 With semiconductors we either provide enough voltage to allow them to conduct electricity on or 1 or we don t apply a voltage and the semiconductor cannot conduct electricity off or 0 The most important property of a semiconductor is the minimum distance between the valence and the conduction band because this represents the amount of energy needed to turn on the semiconductor and enable to conduct electricity This is called the band gap energy 39 1
33. y just stating an answer you may already know looking it up online or asking your TA Below you are given three prompts hypothesizing planning observations data calculations conclusion Your job is to figure out the answer using these prompts as your problem solving model In the event that you should run out of time you may not discover the correct answer but you should make an attempt at each prompt Grades are based on honest effort Your open ended solution should probably include some of the following items sketches of circuit diagrams tables of data calculations recorded observations random ideas etc Write at the prompts on the next page 28 5 1 hypothesizing planning 5 2 observations data 5 3 calculations conclusion the physics 241 laboratory TA have examined this student s Weekly Activity pages and found them to be thoroughly completed TA signature 29 Post Lab vulture iguana rabbit You must complete this post lab section after you attend your lab You may work on this post lab during lab if you have time and have finished all the other lab sections X 1 Resistors in Series a 10092 p 20002 c Y Y Y a How does the total resistance of the circuit compare to the resistance of each individual resistor smaller larger the same Without equations explain why you expect the total resistance should be this way b Compare the currents at points a b and c in the circuit H
34. y to avoid silly errors when trying to rearrange the equation R 2 There is no reason to suspect a priori that the ratio of should be the same for different voltages Therefore a particular component may have different resistances for different applied voltages For example a diode will have a very large resistance until the applied voltage potential difference reaches a certain value and then drop to nearly zero for larger voltages Components that have a resistance that depends on the voltage applied are called non ohmic For introductory students we usually work with ohmic devices in most but not all of the labs For an ohmic resistor the equation R AV constant implies the resistance is the same I value no matter what voltage is applied and the current changes with voltage to keep the ratio AV T constant It should be noted that resistance of a material often depends on its temperature Since a light bulb gets hotter as more voltage is applied across it and so more current flows through it and it consumes more power P 1 AV the light bulbs resistance grows with its brightness So a light bulb definitely is non ohmic 0 A 4 If a 1 5 volt battery is discharged through a 2 5 Q resistor what is the current through the resistor Real batteries have internal resistances that affect their performance by decreasing their effective voltage For example if you take a 1 5 V battery and attach a 0 000001 oh
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