Electrical Engenieering Final Exam
I. OBJECTIVES
1. To analyze a reactive AC circuit and determine its Thevenin Equivalent Circuit
2. To analyze a reactive AC circuit and determine the Maximum Power Transfer load and values
3. Use MultiSim to simulate the reactive AC circuits and validate our calculations
4. Build and take measurements on the reactive AC circuit to validate our predicted results
II. PARTS LIST
Equipment
IBM PC or Compatible
Function Generator
DMM (Digital Multimeter)
Parts
1–2.2 kΩ Resistor 1–4.7 mH Inductor
1–5.1kΩ Resistor 1–10kΩ resistor
Misc Capacitors
Software
MultiSim 11
III. PROCEDURE
A. Theoretical Analysis
1. Given the circuit in Figure 1, calculate the values for the load voltage and current. Since the selfresistance of the inductor is so small compared to all other resistances/reactances, it can be ignored for your calculations.
V_{L} = _____ I_{L} = _____
2. Calculate the values for the Thevenin Equivalent Circuit, Z_{TH} and V_{TH}. Be sure to include both magnitude and phase values in your solution. Assume that the load will be placed where R_{L} is located for your analysis.
Figure 1: Thevenin Example Circuit
V_{TH} = _____ Z_{TH} = _____
(Use polar forms for these values.)
3. Based on your calculations for Z_{TH}, what are the associated resistive and reactive values that comprise the equivalent impedance? Indicate whether it is capacitive or inductive by circling the correct choice below. Also calculate the associated component value for that reactive component.
R = _____ X_{C} / X_{L} = _____ C / L = _____
4. Based on your Thevenin Equivalent Circuit calculations, what load impedance would you choose in order to achieve maximum power transfer? Again, circle your X_{C} /X_{L} choice and include the component value.
R = _____ X_{C} / X_{L} = _____ C / L = _____
5. Based on this choice of load impedance, what will the maximum power equal?
P_{MAX }= _____
B. MultiSim Simulation and Circuit Calculations
1. Launch MultiSim and build the circuit schematic shown in Figure 1.Insert DMMs in the correct locations to measure load current and voltage.
2. Activate the simulation and measure the load voltage and current.
V_{L} = _____ I_{L} = _____
3. Do these values agree with those obtained in Part A, Step 1?
(YES or NO)
Explain why your answer is what it is.
4. Now, build a new circuit in MulitSim that uses your calculated values for V_{TH} and Z_{TH}. This is depicted in Figure 2. You will of course use the calculated values for R and the reactive component (either an inductor or a capacitor) found in Part A, Step 3. Connect the 10 kΩ load to the circuit. Include DMMs to measure load voltage and current.
Figure 2: Thevenin Equivalent Connection
5. Activate the simulation and measure the load voltage and current.
V_{L} = _____ I_{L} = _____
6. Do these values agree with those obtained in Part B, Step 3? (i.e., Is the Thevenin Circuit truly equivalent?)
(YES or NO)
Explain why your answer is what it is.
7. Now replace the 10 kΩ load with the resistor and reactive component you found for maximum power transfer (Part A, Step 4).
8. Activate the simulation and measure the load voltage and current.
V_{L} = _____ I_{L} = _____
9. Based on these measurements, calculate the maximum power transfer.
P_{MAX }= _____
10. Does this value agree with the value obtained in Part A, Step 5?
(YES or NO)
Explain why your answer is what it is.
C. Construction and Analysis of a SeriesParallel Circuit
1. Construct the circuit in Figure 1.
2. Activate the circuit and measure the load voltage and current.
V_{L} = _____ I_{L} = _____
3. Are these the same as the simulated and calculated values?
(YES or NO)
If you answered NO, explain why you think they differ.
4. Now, disconnect the load resistor and measure V_{TH} as shown in Figure 3.
Figure 3: Measuring V_{TH}
V_{TH} = _____
5. Does this value agree with the value obtained in Part A, Step 2?
(YES or NO)
Explain why your answer is what it is.
6. Measuring Z_{TH} requires an indirect method to determine its value. Connect the circuit as shown in Figure 4. We will be using Ohm’s Law to indirectly determine the value for Z_{TH}.
Figure 4: Measuring Z_{TH}
Notice that we have shorted out the original power supply—the standard first step used to determine Z_{TH}. Then, we applied a source and series resistance to the righthand side of the circuit. We are going to use this voltage and current measured through R3 to determine Z_{TH}. R3 is very small compared to the rest of the circuit’s parameters, so it does not significantly affect the circuit’s operation.
7. Measure and record the voltage found across R3. Calculate the current using Ohm’s Law.
V_{R3} = _____ I_{R3} = _____
8. Because I_{R3} is the same as the source current, we can now calculate Z_{TH} = 5 V_{RMS}/I_{R3}
_{ }
Z_{TH} = _____
_{ }
9. Using two oscilloscope probes, measure the angle associated with Z_{TH}. This will be the angle between the applied voltage and the voltage across R3. That is, one scope probe goes across the applied voltage source; the other goes across R3. Be sure to connect both scope ground clips to the same ground point.
_____
10. Do these values (Z_{TH} & ) agree with those obtained in Part A, Step 2?
(YES or NO)
Explain why your answer is what it is.
11. Obtain components close to the values that you calculated in Part A, Steps 3 and 4. Rewire the circuit as it is shown in Figure 2, using the calculated components for Z_{TH} and the maximum power transfer load. Record your chosen values in Table 1, Case #1.
12. Measure the load’s voltage and calculate the power. Record these values in Table 1.
13. Choose a number of different capacitor values from your kit to replace the one you are using for your load impedance. Measure and record the voltages. Calculate the associated power. Record your choices and findings in Table 1. You should do this with four different combinations of R_{L} and C_{L}.
Case #  R_{L}  C_{L}  X_{C}  Z_{L}  V_{L}  P_{L} 
1 






2 






3 






4 






5 






Table 1: Maximum Power Transfer
14. Does Case #1 give you the maximum power in the Table?
(YES or NO)
Explain why your answer is what it is.
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