Superposition Theorem Lab.docx 6p3i6j

EE221 BASIC ELECTRICAL ENGINEERING LAB 3 SUPERPOSITION THEOREM 1.

OBJECTIVE

The objective is to demonstrate the use of the Superposition Theorem in the analysis of circuits with more than one voltage source. 2.

EQUIPMENT Agilent E3630A Triple output supply, Agilent 34405A DMM, ProtoBoard Resistors: 1 x 470R, 1x 680R, 1 x 1k

3.

INTRODUCTION

To superimpose is to lay one thing on top of another. The Superposition Theorem is a means by which we can solve circuits which have more than one independent source. Each source is taken one at a time and all other sources are replaced by their internal resistances. An ideal independent voltage source has zero internal resistance and an ideal independent current source has infinite internal resistance. We shall assume that all our dc voltage supply sources in the lab have zero internal resistances, that is we shall replace them with short circuits. The required voltages or currents are computed for each source acting alone and the combined voltages or currents are found by taking the algebraic sum of the values obtained when each source acted separately. It is therefore necessary to keep ing for the directions of currents and polarities of voltages when using Superposition. 4.

THEORY

Evaluate the currents and voltages in all the resistors shown in Fig.1 using: (a) KCL (b) Superposition Theorem R1

R2

A 470Ω V1

Fig.1

5V

B

C

680Ω R3 1kΩ

V2 10 V

D

5.

PROCEDURE

5.1

The Agilent E3630A DC triple output supply you have been provided with has three adjustable output voltages: 0-6V, 0 to +20V and 0 to -20V. The three supplies share one common terminal marked COM. and also share one switchable voltmeter. Adjust the 0-6V supply to give 5V and the 0 to +20V supply to give 10V, switching the meter to read voltage of the appropriate supply.

5.2

Measure the actual values of the three resistors you have been given.

R1

R2

A 470Ω V1

5V

C

680Ω R3 1kΩ

Fig.2 B

D

5.3

Construct the circuit shown in Fig. 1. Temporarily disconnect the 10 V source and place a jumper across the terminals C and D as shown in Fig. 2. This short circuit represents the internal resistance of the 10 V supply,. Measure the voltages in all the resistors noting the polarity of each one of them and on your drawing of Fig.2 indicate all the voltages and their polarities.

5.4

Since we have already measured the voltages we can use Ohm’s Law to calculate the values of the currents through each resistor using the voltage measured and the actual value of the resistors. This avoids having to break the circuit in order to insert an ammeter. Calculate the current and indicate their values and directions on your drawing of Fig. 2. Tabulate also the voltages and the calculated currents in the resistors..

5.5

As a further check, remove the 5V supply and measure the total resistance looking into the circuit from the terminals A and B with C and D still short circuited. The current in the resistor R1 can then also be found by dividing 5V by the resistance measured when looking into A and B. How does this compare with the current through R1 calculated 5.4 ?

5.6

Repeat steps 5.3 to 5.5 with only the 10 V supply in the circuit, and the 5 V supply disconnected and replaced with a jumper (short circuit) across A and B. You should make your own drawing (Fig. 3) similar to Fig. 2 and indicate the measured voltages with their polarities and calculated currents and their directions in your drawing. Also tabulate these values.

5.7

For each resistor , separately compute the algebraic sum of the voltages and currents when the 5 V and 10 V supplies are acting alone. Tabulate your results

5.8

Now connect the two power supplies in to your circuit exactly as in Fig. 1and measure the voltages and currents when the two supplies are both used, noting also the polarity of each voltages. Tabulate these results.

6.

DISCUSSION

Compare the results obtained in 5.7 and 5.8. Is the Superposition Theorem verifiedby your results? Explain to what extent. 7.

FURTHER INVESTIGATION AND CONCLUSION

From your measurements compute the power in each resistor for the two cases when each two supply acting separately and the case when there are two acting together. Is the superposition theorem valid for powers as well? Explain your answer and write a suitable conclusion.