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 self-resistance of the inductor is so small compared to all other resistances/reactances, it can be ignored for your calculations.

VL = _____                                  IL = _____

2.     Calculate the values for the Thevenin Equivalent Circuit, ZTH and VTH. Be sure to include both magnitude and phase values in your solution. Assume that the load will be placed where RL is located for your analysis. Figure 1: Thevenin Example Circuit

VTH = _____                ZTH = _____

(Use polar forms for these values.)

3.     Based on your calculations for ZTH, 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 = _____          XC / XL = _____       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 XC /XL choice and include the component value.

R = _____          XC / XL = _____       C / L = _____

5.     Based on this choice of load impedance, what will the maximum power equal?

PMAX = _____

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.

VL = _____                                  IL = _____

3.     Do these values agree with those obtained in Part A, Step 1?

(YES or NO)

4.     Now, build a new circuit in MulitSim that uses your calculated values for VTH and ZTH. 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.

VL = _____                                  IL = _____

6.     Do these values agree with those obtained in Part B, Step 3? (i.e., Is the Thevenin Circuit truly equivalent?)

(YES or NO)

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.

VL = _____                                  IL = _____

9.     Based on these measurements, calculate the maximum power transfer.

PMAX = _____

10.  Does this value agree with the value obtained in Part A, Step 5?

(YES or NO)

C.  Construction and Analysis of a Series-Parallel Circuit

1.     Construct the circuit in Figure 1.

2.     Activate the circuit and measure the load voltage and current.

VL = _____                                  IL = _____

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 VTH as shown in Figure 3.

Figure 3: Measuring VTH

VTH = _____

5.     Does this value agree with the value obtained in Part A, Step 2?

(YES or NO)

6. Measuring ZTH 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 ZTH.

Figure 4: Measuring  ZTH

Notice that we have shorted out the original power supply—the standard first step used to determine ZTH. Then, we applied a source and series resistance to the right-hand side of the circuit. We are going to use this voltage and current measured through R3 to determine ZTH.    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.

VR3 = _____   IR3 = _____

8.     Because IR3 is the same as the source current, we can now calculate ZTH = 5 VRMS/IR3

ZTH = _____

9.     Using two oscilloscope probes, measure the angle associated with ZTH. 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 (ZTH &  ) agree with those obtained in Part A, Step 2?

(YES or NO)

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 ZTH 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 RL and CL.

 Case # RL CL XC |ZL| VL PL 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)  