# UNIVERSITY F P RTLAND Sch l f Engineering

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1 UNIVERSITY F P RTLAND Sch l f Engineering EE271-Electrical Circuits Laboratory Spring 2004 Dr. Aziz S. Inan & Dr. Joseph P. Hoffbeck Lab Experiment #4: Electrical Circuit Theorems - p. 1 of 5 -

2 Electrical Circuit Theorems I. Objective In this experiment, the students will analyze, construct and test dc resistive circuits to gain further insight and hands-on experience on electrical circuits as well as to verify some of the circuit theorems they learn in class such as the Superposition Principle, Thevenin and Norton Equivalent Circuits and Maximum Power Transfer Theorem. II. Procedure PART 1: Superposition Principle Pre-lab Assignment 1.a: For the circuit shown in Fig. 1, calculate the voltage V 2 across the resistor R 2 using the superposition principle. Pre-lab Assignment 1.b: For the circuit shown in Fig. 1, reverse the polarity of the 5 V dc voltage source and redo pre-lab assignment 1.1. R 1.2 R 3 =2.4 V S1 =7.5 V I 2 R 2.2 V 2 V S2 Fig. 1. A resistive circuit excited by two dc voltage sources. Lab Experiment 1.a: Construct the resistive circuit shown in Fig. 1. Measure and record the actual values of the resistors R 1, R 2, and R 3 used in your circuit. To verify the superposition principle, measure and record the voltage V 2 for three cases: - p. 2 of 5 -

3 (a) When V s1 voltage is on and V s2 is off. (Voltage source off means you disconnect the voltage source from the circuit and short the terminals in your circuit where this voltage source was connected. Warning: Do not short the terminals of the voltage source itself!) (b) When V s1 voltage is off and V s2 is on. (c) When both V s1 and V s2 voltages are on. Check to see if superposition holds. Also check to see if your measured V 2 values agree with the V 2 values calculated in your pre-lab assignment 1.a. Lab Experiment 1.b: Reverse the polarity of the 5 V voltage source in your circuit and repeat the same V 2 measurements done in Lab Experiment 1.a, parts (a), (b) and (c). Check to see if superposition holds. Also check to see if your measured V 2 values agree with the V 2 values calculated in your pre-lab assignment 1.b. PART 2: Thevenin, Norton & the Maximum Power Transfer Theorem Pre-lab Assignment 2.a: For the circuit shown in Fig. 2, find the Thevenin and Norton equivalent circuits seen between terminals A and B. Draw each equivalent circuit separately with the appropriate values provided. R 1 R 3 A V S R 2 V OC B Fig. 2. The resistive circuit to be replaced by a Thevenin circuit. Pre-lab Assignment 2.b: For the circuit shown in Fig. 2, find the optimum value of the external load resistance R L,opt to be connected between the terminals A and B so that it receives maximum power from the circuit. What is P L,max? (Hint: Use the results of pre-lab assignment 2.a.) - p. 3 of 5 -

4 Lab Experiment 2.a: Construct the circuit shown in Fig. 2. Measure and record the actual values of the resistors used in your circuit. Verify the Thevenin and Norton equivalent circuits obtained in pre-lab assignment 2.a by measuring the open-circuit voltage V OC and the short-circuit current I SC between terminals A and B. Lab Experiment 2.b: Connect a load resistance with the optimum value R L,opt between terminals A-B in the original circuit shown in Fig. 2. Measure the voltage V L across R L,opt and use it to verify the P L,max value calculated in pre-lab assignment 2.b. PART 3: Maximum power to a load resistance with fixed value Pre-lab Assignment 3: In Fig. 3, assume that the load resistance R L has a fixed value given by R L kω. (a) How much power is being delivered to R L? (b) Your job is to introduce a single external resistor R ext into the circuit with an appropriate value to maximize power delivery to the 1 kω load. What is the value of R ext? Where should it be connected? What is P L,max? (Note that this problem is different than the maximum power transfer theorem.) Lab Experiment 3: Verify the results of pre-lab assignment 3 experimentally. Measure and record the load voltage V L and the current I L with and without the external resistance connected and calculate the load power using P L =V L I L in each case. Approximately how much percent did the load power increase due to the introduction of the external resistance R ext into the circuit? 3 I L V S R L V L Fig. 3. A circuit with a fixed load resistance having a value R L kω. - p. 4 of 5 -

5 III. Discussions & Conclusion In this section, discuss the various aspects of Experiment # 4 and make some conclusions. In your write-up, you should at least address the following questions: 1. What was the objective of this experiment and was the objective achieved? 2. Did any of your measurements have more than 5% error? What was your maximum % error? 3. What sources of error may have contributed to the differences between the theoretical values and the measured values? 4. Other comments relevant to this experiment. - p. 5 of 5 -

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