Electrical circuits and simulation lab manual

electrical circuits and simulation lab manual pdf electrical circuits laboratory manual
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LABORATORY MANUAL ELECTRICAL MEASUREMENTS and Circuits EE 2049 Khosrow Rad 2016 DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING CALIFORNIA STATE UNIVERSITY, LOS ANGELES Published July 13, 2016 1 Digital Multimeter Resistance Measurement EXPERIMENT 1 Here is the resistor color code: Color First Stripe Second Stripe Third Stripe Fourth Stripe Black 0 0 x1 Brown 1 1 x10 Red 2 2 x100 Orange 3 3 x1,000 Yellow 4 4 x10,000 Green 5 5 x100,000 Blue 6 6 x1,000,000 Purple 7 7 Gray 8 8 White 9 9 Gold 5% Silver 10% None 20% If the following color comes in third stripe it will act as Gold = decimal multiplier =10-1 = 0.1 tolerance Silver = decimal multiplier =10-2 = 0.01 tolerance No color = decimal multiplier = tolerance 1. Obtain about 15 resistors of the 15 KΩ value. Measure the resistance of each resistor using the DMM range that will give the maximum number of significant figures. Draw a distribution graph with the vertical axis being the number of resistors within each 1 % range and the horizontal axis being the percent deviation from the nominal resistance value. Make you table for all 15 resister same as table 1. 3 2. Obtain a Resistance Substitution Box and use a DMM to measure the resistance values for all of the resistance settings to the maximum number of significant figures. Compare the actual resistance values to the nominal values in terms of the percent difference. 3. Connect short lead or jumper wire using your red and black wire between the DMM input terminals and read the resistance, using the lowest resistance range to obtain the maximum number of significant figures. Now connect long lead wire to the DMM and repeat the measurement. Calculate the approximate values of resistance per foot of the lead wire. Use the DMM NULL for an easier measurement of this. 4. Variable Resistors: Obtain a 5000 Ω variable resistor (potentiometer or rheostat). a) Measure the total (i.e. end-to-end) resistance. b) Measure the resistance between the "wiper arm” and one end with the knob in the fully clockwise position, and then with the knob in the fully counter-clockwise position. Then repeat this for the resistance between the wiper arm and the other end of the resistor. 5. In some cases, especially when using the DMM to measure resistance values associated with various electronic devices, it is important to know the voltage produced by the DMM when measuring resistance. Connect the DMM to a resistance substitution box and for every DMM resistance range adjust the resistance to give a reading as close to the full-scale resistance reading as possible. Connect a second DMM set to read voltage across (in parallel with) the first DMM and reading the test voltage of the first DMM. 6. OUESTIONS: a) Give the color codes for the following resistors: i) 2 Ω, 5% ii) 0. Ω, 5% iii) 1 k Ω, 20% b) The highest resistance range on a DMM is 20 MΩ. To measure a very large unknown resistor Rx, the unknown resistor is placed in parallel with a resistor that has previously been measured and has an actual value of 19.95 M Ω. The resulting DMM reading is 18.16 MΩ. Find the value of Rx 4 DIGITAL MULTIMETER: D-C VOLTAGE and D-C Current MEASUREMENT EXPERIMENT 2 1. Connect the Digital Multimeter (DMM) to a DC Power Supply as show in Figure below . Set the DMM to read DC VOLTS. 2. Connect a Resistance Substitution Box in series between the DC Power Supply and the DMM. Set the resistance value to a low setting of 1 KΩ. Carefully adjust the DC Power Supply to give a reading of 10V on the DMM. Now read the DMM for the following values of series resistance: 10 MΩ, 4.7 MΩ, 1 MΩ, and 100 KΩ. From these readings, use voltage division to calculate R , the equivalent internal resistance of the voltmeter. Vi 3. QUESTIONS: a) Define "resolution", "accuracy", and "precision" and explain the differences (if any) among these three terms. b) What is the difference between the "nominal" and the "actual" value of an electronic component? Measure DC resistance of the DMM Ammeter: Ammeters also have an internal electrical resistance. Ideally an ammeter would have no resistance (0 Ω) so that it would not alter the current flow it is trying to measure. In this exercise you will measure the DC resistance of the real DMM ammeter. Set up the circuit as shown in Figure 2. Using the DMM for the ammeter 5 Figure 2 Set the resistor R to 1 MΩ resistance. And record the resistance R and the current indicated by the ammeter. f. Adjust R to 100kΩ. In your table, record the resistance R and the current indicated by the ammeter. g. Continue to decrease the resistance R until the ammeter reading drops by a significant fraction (up to about one half) of the original value. Record the final resistance R and measured current. Use the DMM ohmmeter to measure the actual final resistance R, rather than relying on the indicated settings of the substitution box. (You will need to connect the DMM cables to “VΩ” and “COM” for this measurement.) i. From these readings, use current division to calculate RAi, the equivalent internal resistance of the ammeter. 5. Questions a) What is the input resistance of an ideal current-measuring DMM? b) What is the input resistance of an ideal voltage-measuring DMM? c) How must a DMM be connected in a circuit to measure current: In series or in parallel? d) How must a DMM be connected in a circuit to measure voltage: In series or in parallel? e) Under what conditions will the voltage burden or the input resistance of the DMM produce a significant error in current measurement? 6 Voltage Regulation and AC Power Supply EXPERIMENT 3 A. VOLTAGE REGULATION 1. Connect the DC Power Supply to the Digital Multimeter (DMM) and set the DC Power Supply to give an output voltage of 10V as read on the DMM. Read and record the DC voltage to the maximum number of significant figures. 2. Connect a 50 Ω, 10 watt resistor across the DC Power Supply. Record the new value of the voltage. (Use the NULL for an easier measurement.) 3. Calculate the voltage regulation of the DC Power Supply as defined by voltage regulation = (no-load voltage) - (full-load voltage/ (no-load voltage) x 100% The no-load voltage is the output voltage of the DC Power Supply when the output current is zero. The full-load voltage in this case is the output voltage when the output current is 10V/50 Ω = 200 mA. 4. Calculate the output resistance R of the DC Power Supply from the relationship 0 R = (no-load voltage) - (full-load voltage) / (full-load current) - (no-load current) AC 0 RIPPLE FACTOR 5. Set the DMM to read AC voltage. Read and record the AC voltage (in millivolts). Do this for both the full- load (50 Ω) and the no-load conditions. Calculate the DC Power Supply ripple factor as given by Ripple factor = AC Ripple Voltage / DC Output Voltage x 100% 6. QUESTIONS: a) What does a DC Power Supply do? b) Why is there an AC ripple present, and will a battery have an AC ripple? c) If a DC Power Supply has an output resistance of 10 mΩ (milli-ohms) and a no-load output voltage of 10V, find the change in the output voltage and the load regulation for a full-load output current of 1 A. d) A DC Power Supply is adjusted to give a no-load output voltage 10V. The AC line voltage is 115V RMS. When a full-load current of 1 A is drawn, the output voltage drops to 9.98V. Find the no-load to full-load load regulation expressed in percent. e) When the AC line voltage drops from 11 5V to 110V, the DC output voltage decreases from 10V to 9.95V. Find the line regulation expressed in terms of %/V. f) If the DC output voltage is 10V and RMS AC ripple voltage on the output is 10 mV, find the percentage ripple factor. 7 g) As the temperature varies from 25 °C to 35 °C, the output voltage increases from 10V to 10.05V. Find the temperature coefficient of the output voltage expressed. B. AC Power Supply Connect a Digital Multimeter (DMM) to a FUNCTION GENERATOR. Set the DMM function control to read AC voltage. Adjust the frequency control of the FUNCTION GENERATOR to 1 kHz. Adjust the amplitude control to give an output voltage of 1V RMS as read on the DMM. Compare the volts peak-to-peak (VPP) reading on the FUNCTION GENERATOR to the DMM reading. Are they consistent? 1. Increase the frequency up to the point where the DMM reading has changed by about 10%. 2. Now reduce the frequency of the Function Generator to below 1 kHz, and decrease the frequency to the point where the DMM reading has changed by about 10%. 3. DMM Input Impedance Set the FUNCTION GENERATOR frequency to 100 Hz and adjust the output voltage to 1V RMS. Connect a 1 MΩ resistor in series between the FUNCTION GENERATOR and the DMM. Now increase the frequency 100 kHz. Read the DMM, and from the reading calculate the DMM input capacitance. 8 FUNCTION GENERATOR and OSCILLLOSCOPE EXPERIMENT 4 1. a) Connect a Digital Multimeter to the Function Generator. Connect a fixed resistor across (i.e. in parallel with) the output of the Function Generator. Set the frequency to 1 kHz and the output voltage to 1.0 V. Change the resistance until the output voltage is down to about one-half of its original value. Record the voltage and resistance values. 2. Calculate the output resistance of the Function Generator. Compare with the specifications. 3. What value of output resistance would the "ideal" Function Generator have? Explain. 4. QUESTIONS a) A Function Generator is adjusted to give a no-load (open-circuit) voltage of 1.0V. When a 1 K Ω load is placed across the output terminals of the Function Generator the output voltage drops to 0.8 V. Find the output resistance of the Function Generator. Voltage Ratio in decibels (dB) = 20 log10 (V1/V2) b) Express the following ratios in decibels (dB): i) V V =100 2 1/ ii) V V = 0.1 2 1/ c) Change these dB values to voltage ratios i) -10dB ii) 3dB d) A Function Generator has a specification that the variation in the output voltage with frequency will remain flat to within ± 1 dB over the frequency range of 10 Hz to 100 kHz. Find the corresponding maximum percentage variation in the output voltage over this frequency range. B. OSCILLLOSCOPE Connect the Function Generator main output to the Channel 1 input of the oscilloscope and to a DMM (all in parallel). Connect the Function Generator sync (synchronization) output to the Channel 2 input of the oscilloscope. 1. Set the Function Generator to give a sine wave output at a frequency = 1 kHz. Adjust the amplitude to give a peak-to-peak voltage of 2V as observed on the oscilloscope. Press the Autoscale button on oscilloscope for the initial settings. Import oscilloscope display to computer. Then display only the sine wave on Channel 1. a) Import oscilloscope display to computer b) Compare the peak-to-peak voltage as measured by counting divisions and using the voltage/DIV scale to that obtained from the oscilloscope direct voltage measurement. 9 c) Record the RMS voltage as observed on the DMM. Compare that to the RMS voltage as measured by the oscilloscope. d) Compare the RMS voltage with the expected value based on the peak-to-peak voltage. e) Measure the period of the waveform by counting divisions and using the time/DIV scale. Find the frequency and compare to the expected value. f) Obtain the period of the waveform using the oscilloscope direct measurement. Compare to the value obtained by counting divisions and using the time/DIV scale. g) Obtain the frequency of the waveform using the oscilloscope direct measurement. Compare with the value set on the Function Generator. 2. Set the Function Generator to give a square wave output at a frequency = 1 kHz with an amplitude of 2V peak-to-peak voltage as observed on the oscilloscope. h) Import oscilloscope display to computer i) Compare the peak-to-peak voltage as measured by counting divisions and using the voltage/DIV scale to that obtained from the oscilloscope direct voltage measurement. j) Record the RMS voltage as observed on the DMM. Compare that to the RMS voltage as measured by the oscilloscope. k) Compare the RMS voltage with the expected value based on the peak-to-peak voltage. l) Measure the period of the waveform by counting divisions and using the time/DIV scale. Find the frequency and compare to the expected value. m) Obtain the period of the waveform using the oscilloscope direct measurement. Compare to the value obtained by counting divisions and using the time/DIV scale. n) Obtain the frequency of the waveform using the oscilloscope direct measurement. Compare with the value set on the Function Generator. 3. Set the Function Generator to give a square wave output at a frequency = 1 kHz with an amplitude of 2V peak- to-peak voltage as observed on the oscilloscope. a) Import oscilloscope display to computer b) Compare the peak-to-peak voltage as measured by counting divisions and using the voltage/DIV scale to that obtained from the oscilloscope direct voltage measurement. c) Record the RMS voltage as observed on the DMM. Compare that to the RMS voltage as measured by the oscilloscope. 10 d) Compare the RMS voltage with the expected value based on the peak-to-peak voltage. e) Measure the period of the waveform by counting divisions and using the time/DIV scale. Find the frequency and compare to the expected value. f) Obtain the period of the waveform using the oscilloscope direct measurement. Compare to the value obtained by counting divisions and using the time/DIV scale. g) Obtain the frequency of the waveform using the oscilloscope direct measurement. Compare with the value set on the Function Generator. 4.Set the DMM to read DC volts. Turn on the DC OFFSET control on the Function Generator and rotate it to give a DC offset of +1V. Measure the shift in the DC level on the oscilloscope and compare with the value of DC voltage indicated by the DMM. Set the DMM to read AC volts. What is the change in the DMM AC voltage reading as the DC offset is changed from zero to +1V? 5.Repeat the previous procedure with a DC offset of -1V. 6..Change the input coupling switch to AC and now observe what happens 7.Set the Function Generator back to a SINE WAVE output. Change the Trigger slope to NEGATIVE SLOPE and observe what happens. Now change the TRIGGER SLOPE to POSITIVE SLOPE and observe the result. 7.Change the sweep speed control (TlME/DlV) to 0.5ms/DIV. Measure the period and compare with the previous result. 8.Repeat the previous procedure for sweep speeds (TIME/DIV) of 1.0 ms/DIV, 2.0 ms/DIV, and 0.1 ms/DIV. 9.Set sweep speed to 1 ms/DIV. Measure the period for the following frequencies and compare with the expected values: 2 kHz, 4 kHz, and 10 kHz. 11 OSCILLOSCOPE OPERATION EXPERIMENT 5 A. X-Y DISPLAY 1. Set up the oscilloscope for an X-Y display. Connect one Function Generator to the CH 1 input to be displayed on the Y- axis, and a second Function Generator to the CH 2 input to be displayed on the X-axis. Set the frequency of the second Function Generator to 100 Hz. Set the output voltage level of the second Function Generator to give a peak-to-peak voltage of 6V. 2. Adjust both Function Generators to produce a circle on the screen with a diameter of 6V. Sketch and dimension the display and record the Function Generator settings. 3. Adjust both Function Generators to produce an ellipse on the screen with a major axis (X-axis) of 6V and a minor axis (Y-axis) of 2V. Sketch and dimension the display and record the Function Generator settings. 4. Adjust both Function Generators to produce a diamond-shaped figure on the screen with a major axis (X-axis) of 6V and a minor axis (Y-axis) of 6V. Sketch and dimension the display and record the Function Generator settings. 5. Adjust both Function Generators to produce a diamond-shaped figure on the screen with a major axis (X- axis) of 6V and a minor axis (Y-axis) of 2V. Sketch and dimension the display and record the Function Generator settings. 6. Adjust both Function Generators to produce a diamond-shaped figure on the screen with a major axis (X- axis) of 2V and a minor axis (Y-axis) of 6V. Sketch and dimension the display and record the Function Generator settings. 7. Adjust both Function Generators to produce a pattern of dots on the screen with a spacing of 4V between dots in both directions. Sketch and dimension the display and record the Function Generator settings. 8. Adjust both Function Generators to produce a "figure 8" pattern on the screen with the "figure 8" being 6V high and 4V wide. Sketch and dimension the display and record the function Generator settings. 9. Adjust both Function Generators to produce a horizontal (i.e. sideways) "figure 8" pattern on the screen with the "figure 8" being 4V high and 8V wide. Sketch and dimension the display and record the Function Generator settings. B. OSCILLOSCOPE DUAL CHANNEL DISPLAY 1. Connect a Function Generator to both the CH 1 and CH 2 Input terminals of the oscilloscope. Set input coupling switches to DC for both channels. Set the Function Generator to give a SQUARE WAVE output voltage waveform with a peak-to-peak amplitude of 5V and a frequency of 10 kHz. The oscilloscope sweep speed should be set to 10 µs/DIV. Adjust the vertical controls of both channels such that the two displays overlap exactly. Oscilloscope Dual Channel Operation 2. Now insert an R-C low-pass network between the Function Generator and the CH 2 input of the oscilloscope. 12 The RC network consists of a Resistance Substitution Box (R ) and a Decade Capacitor Box, Type CDA (C ) as 1 1 shown in the diagram below. Start off with the resistance set to 10 KΩ and the capacitance set to zero. The input -voltage of the R-C network is displayed on CH 1 and the output voltage will be displayed by CH2. Measurement of the Time Domain Response Characteristics 3. Increase the capacitance and observe the results on the oscilloscope. Find the time it takes the output voltage to go from zero to 63.2% of the input voltage for four different values of capacitance. Decrease the frequency as necessary to display the full transient response curve. Compare the zero to 63.2% rise time with the R-C time constant (i.e. the R-C product). Repeat this procedure for the 100% to 36.8% faIl time. 4. Set the resistance to zero and the capacitance to 1 nF (0.001 µF). Now increase the resistance and observe the results on the oscilloscope. Decrease the frequency as necessary to display the full transient response curve. Find the time it takes the output voltage to go from zero to 63.2% of the input voltage for four different values of resistance. Compare the zero to 63.2% rise time with the R-C time constant. Repeat this procedure for the 100% to 36.8% fall time. 5. Set the resistance to 10 KΩ and the capacitance to 0.001 µF. vary the frequency of the Function Generator from about 100 Hz to about 1 MHz and observe the results. Find the frequency at which the output voltage reaches only 10% of the input voltage. Under these conditions the pulse width should be approximately equal to 1/10 of the R-C time constant. Compare the time constant to the pulse width. 6. Set the Function Generator to produce a SINE WAVE output. Set R to 10 KΩ and C to 0.001 µF. vary the 1 1 frequency of the Function Generator from about 100 Hz up to about 2 MHz and compare the input and output waveforms. 7. Find the frequency at which the output voltage has decreased to 70.71 % of the input voltage. Find the phase angle between the output and input waveforms at this frequency. Compare the frequency and phase angle with the expected values. Repeat this procedure for the frequency at which the output voltage has decreased to 50% of the input voltage, and then for the frequency at which the output voltage is only 10% of the input voltage. 8. QUESTIONS For most electronic systems the relationship between the 3 dB bandwidth (BW) and the rise time (10% to 90%) is given approximately by RISE TIME x BW = 0.35. Note: If a signal passes through several systems in series, (i.e. cascaded) the rise time at the output is given approximately as the square root of the sum of the squares of the rise times of the individual systems. a) An oscilloscope has a 35 MHz BW. Find the apparent rise time of the oscilloscope display if the signal input to the oscilloscope is an ideal pulse waveform. b) An oscilloscope has a 35 MHz BW. The oscilloscope is connected directly to a Pulse Generator and the oscilloscope display shows a rise time of 15 ns. Find the rise time of the Pulse Generator 13 output. c) A Pulse Generator produces a pulse waveform output with a 10 ns rise time. After the pulse signal has passed through some electronic system it is displayed on the screen of a 35 MHz oscilloscope. The oscilloscope display shows a rise time of 25 ns. Find the rise time and the 3 dB BW of the electronic system. d) The input voltage of a system is displayed on CH 1 of an oscilloscope and the output voltage is displayed on CH 2. Both waveforms are sinusoidal with a period of 1 ms. The CH 2 waveform lags behind the CH 1 waveform by 0.1 ms. Find the phase shift produced by the system under study. Express the answer in degrees and in radians PSpice Analysis of DC Circuits EXPERIMENT 6 14 OBJECTIVES Use PSpice Circuit Simulator to check laboratory circuits and homework problems EQUIPMENT PSpice Program THEORY A dc circuit is a circuit in which the voltages of all independent voltage sources and the currents of all independent current sources have constant values. All of the currents and voltages of a dc circuit, including mesh currents and node voltages, have constant values. PSpice can analyze a dc circuit to determine the values of the node voltages and also the values of the currents in voltage sources. PSpice uses the name “Bias Point” to describe this type of analysis. The name “Bias Point” refers to the role of dc analysis in the analysis of a transistor amplifier.) In this lab we consider four examples. The first example illustrates analysis of circuits containing independent sources while the second is dependent sources. The third illustrates the use of PSpice to check the node or mesh equations of a circuit to verify that these equations are correct. The final example uses PSpice to compare two dc circuits. There is a six-step procedure to organize circuit analysis using PSpice. This procedure is stated as follows: Step 1. Formulate a circuit analysis problem. Step 2. Describe the circuit using Schematics. This description requires three activities. a. Place the circuit elements in the Schematics workspace. b. Adjust the values of the circuit element parameters. c. Wire the circuit to connect the circuit elements and add a ground. Step 3. Simulate the circuit using PSpice. Step 4. Display the results of the simulation, for example, using probe. Step 5. Verify that the simulation results are correct. Step 6. Report the answer to the circuit analysis problem. Part 1: DC Circuits Containing Independent Sources Part 1A: Capturing and Simulating the DC Circuit Apply the six-step procedure to analyze the circuit shown to determine the value of v , the voltage across the 6Ω 6 resistor. PSpice Circuit R1 3 24.00V 20.00V + V1 R2 V6 I1 24V 6 2A - 0V 0 Part 1B: Verify that the simulation results are correct 15 Use simple circuit methods to verify the results. Is the original circuit equivalent to the PSpice circuits? Use short concise sentences to explain your reasoning. Part 2: DC Circuits Containing Dependent Sources PSpice can be used to analyze circuits that contain dependent sources. The PSpice symbols used to represent dependent sources are labeled as E, F, G and H (see table to the right) and are located in the analogy library. Part 2A: Capturing and Simulate a CCCS Circuit This example illustrates analysis of a circuit that contains a dependent source. Particular attention is paid to preparing the circuit for analysis using PSpice. Suppose that a circuit containing a dependent source is An equivalent PSpice circuit would look like Part 2B: Verify that the simulation results are correct Use simple circuit methods (hint: KCL at each node) to verify the results of v and i. Are the two circuits’ equivalent? Part 3: Mesh and Node Equations In this example, PSpice is used to check node and mesh equations of a circuit. Consider the circuit shown. A set of mesh currents has been labeled and the nodes of this circuit have been numbered. The circuit can be represented by the following node and mesh equations: 17i −−− 8i 2i 5i = 0 12 3 4 23v −= 12v 36 bc −+ 8i 11i − 3i = 12 1 23 −55v + 21v −= 6v 0 b cd −− 7i 3i + 5i + 11i = 0 12 3 4 −+ 6v 26v = 180 c d −4i + 3i += i 0 2 34 Node equations Mesh equations The objective of this example is to use PSpice to determine if these equations are correct. 16 Part 3A: Formulating a circuit with PSpice We have seen that PSpice will calculate the node voltages of a circuit such as the one shown above. The node equations can be checked by determining the values of the node voltages using PSpice and substituting those values into the node equations. PSpice does not calculate mesh currents, but it does calculate the currents in voltage sources. The mesh current i is the current through the 12 V voltage source. PSpice uses the passive 2 convention for all elements, including voltage sources. The voltage source current that PSpice will report is the current direction from + to −. In this case, PSpice will report the value of –i rather than i . Similarly, 0V-voltage 2 2 sources can be added to the circuit to measure the other mesh currents such as mesh currents i , i and i . 1 3 4 Part 3B: Verify that the simulation results are correct One can verify the results by one of the following ways. (i) Substitute the node voltages (mesh currents) from PSpice into the node equations (loop equations) and verify that they satisfy these equations. (ii) Solve the system of equations (for both Node and Mesh) using the matrix operations on your calculator and compare them to the PSpice results. Part 4: Challenge PSpice Circuit A dc circuit with dependent sources is shown. Use PSpice to find the values of i , i and v . x y z What to turn in: turn in all PSpice circuits for each of the parts listed below. Part 1: Determine the voltage v across the 6Ω-resistor using simple circuit techniques and compare it to PSpice calculated value. How do they compare? Part 2: Determine the voltage v across the 5Ω-resistor and the current i through the 6Ω-resistor using simple circuit techniques and compare it to PSpice calculated values. How do they compare? Part 3: Use PSpice to determine the node voltages (v , v , v ) and the mesh (or loop) currents (i , i , i , i ). b c d 1 2 3 4 Substitute these values into the node equations and the mesh equations. Do the PSpice values satisfy these node and mesh equations? Part 4: Use PSpice to determine that the controlling variables (i , i , v ) and verify that the dependent source x y z values are correct. 17 Basic Circuit and Divider Rules EXPERIMENT 7 Part 1 Basic Circuit OBJECTIVES 1. Become familiar and organized Circuit Kit for the semester. 2. Become familiar with a breadboard with the lab power supply and review the measurement of voltage, current, and resistance using a Digital Multimeter (DMM). EQUIPMENT Power supply Part 1: Connection Pattern of the Breadboard a. Set the DMM to OHMS and the range to lowest resistance. Use jumper wires to make connections to the meter. Measure the continuity between different sets of pins to determine which groups of pins are connected and which are not. Lack of continuity will be read as an open circuit by the DMM. b. Set the power supply to 10V and connect it to the breadboard posts. Use jumper cables to transfer the power from the posts to the breadboard pins labeled “+” and “−” at the top of the board. Measure the open-circuit voltages to confirm that the power was transferred. Part 2: Basic Series Measurements Construct the circuit a. Calculate the theoretical equivalent series resistance R using the measured resistor values. S,thy b. Measure the experimental equivalent series resistance RS,expt using a DMM. Use a percent difference to compare the theoretical and experimental values. How do they compare? c. Energize the circuit and measure the current using an ammeter. d. Using the supply voltage and the ammeter reading, calculate the equivalent series resistance R using Ohm’s S,Ohm law. Use a percent difference to compare the R with R from part (2b). How do they compare? S,Ohm S,expt e. Repeat parts (2a-2d) where the voltage has been increased to 30V. 18 Part 3: Basic Parallel Measurements Construct the circuit a. Calculate the theoretical equivalent parallel resistance RP,thy using the measured resistor values. b. Measure the experimental equivalent parallel resistance R using a DMM. Use a percent difference to P,expt compare the theoretical and experimental values. How do they compare? c. Energize the circuit and measure the current using an ammeter. d. Using the supply voltage and the ammeter reading, calculate the equivalent parallel resistance R using P,Ohm Ohm’s law. Use a percent difference to compare the RP,Ohm with RP,expt from part (3b). How do they compare? 19 Kirchhof's Voltage Law and Kirchhof's Current Law EXPERIMENT 8 1. Obtain 6 randomly selected resistors with values between 1.0 Kohm and 10 Kohms. Measure the actual resistance values with a Digital Multimeter (DMM). The resistance range on the DMM should be chosen so as to obtain the maximum accuracy (i.e. maximum number of digits for the DMM reading). Compare the actual resistance values as determined by the DMM with the nominal resistance value as obtained from the color bands on the resistor. Determine If the actual resistance values are within the tolerance limits for each resistor. 2. Construct the circuit shown in Figure 8.1.1. Adjust the supply voltages Vs to +10 Volts. Figure 8.1.1 3. Measure all branch voltages with a DMM. The measurements should be made with the DMM range chosen so as to obtain maximum accuracy (i.e. maximum number of digits) for each branch voltage measurement. Remember to keep proper track of the algebraic signs. 4. Verify that Kirchhof's Voltage Law is satisfied for all of the loops in the circuit. Measure all branch voltages in the circuit with a DMM, Do they add (algebraically) to zero ? Calculate the percentage error based on the following equation: percentage error = ∑ V / (1/2) ∑ V x 100 % Does the percentage error obtained seem reasonable in view of the accuracy of the DMM ? 5. From the branch voltages calculate the branch currents. Remember to use the actual, and not the nominal resistance values for this calculation, Verify that Kirchhof's Current Law is satisfied at every node in the circuit. Calculate the percentage error using the relationship: percentage error = ∑ I / (1/2) ∑ I •100 % Does the percentage error obtained seem reasonable In view of the accuracy of the DMM ? 6. Using network reduction calculate the expected values of all of the branch currents. Compare the branch current values so obtained with the values obtained by the DMM measurements (in step 5). 7.The input resistance of the DMM is 10 Mohms. How much error will this input resistance result in? Will the 20 loading effect of the DMM input resistance account for some of the experimental error in steps 4 and 8.2 SUPERPOSITION THEOREM 1. Using the same circuit as for experiment 1, insert an additional power supply into the last loop as shown in Figure 8.2.1. Figure 8.2.1 Set V1 to +10 V and V2 to +15 V. Double check the values of V1 and V2. 2. Measure all branch voltages with a DMM (maximum place accuracy), Remember to keep track of algebraic signs. 3. Replace V by a short-circuit. Measure all branch voltages. Then put V back into the circuit. 2 2 4. Replace V by a short-circuit. Measure all branch voltages. 1 5. From the above measurements verify that the superposition theorem is satisfied. 6. Using network reduction and the superposition theorem calculate the expected values of all of the branch voltages in the circuit. Compare the calculated values with the measured values. 21