## Search in the document preview

1

*University of Technology
*

*Laser and Optoelectronics Engineering Department
*

*Laser Engineering Branch
*

*Power electronics 2010-2011
*

**Experiment No.12
**

**Superposition Theorem
**

**Aim of experiment**: To study Superposition theorem practically.

**
Apparatus
**1. DC circuit training system
2. Set of wires.

3. DC Power supply

4. Digital A.V.O. meter

**
Theory
**

The superposition theorem is very useful for finding the voltages and currents

in a circuit with two or more sources of supply, and is usually easier to use than

Kirchoff ’s law equations. One supply is selected and the circuit is redrawn to

show the other supply (or supplies) short-circuited (leaving only the internal

resistance of each supply). The voltage and current caused by the first supply can

then be calculated, using **V = RI** methods together with the rules for combining

series and parallel resistors. Each supply is treated in turn in the same way, and

finally the voltages and currents caused by each supply are added.

Hence, this theorem may be state as follows:

**Example: **In the network shown, find the voltage across the 2.2 k resistor.

*In a network of linear resistances containing more than one generator (or
*

*source of e.m.f.), the current which flows at any point is the sum of all the
*

*currents which would flow at that point if each generator were considered
*

*separately and all the other generators replaced for the time being by
*

*resistances equal to their internal resistances. *

2

*University of Technology
*

*Laser and Optoelectronics Engineering Department
*

*Laser Engineering Branch
*

*Power electronics 2010-2011
*

**
Procedure**

**1. **Connect the circuit shown below.**
2. **Measure values of **( I1 , I2 , I3 ) **and record it in the table

I1 (mA) I2 (mA) I3 (mA)

**In this network, there are
**

**two generators and three
**

**resistors. The generators
**

**might be batteries,
**

**oscillators, or other signal
**

**sources.
**

**To find the voltage caused by
**

**the 6V generator, replace the
**

**4V generator by its internal
**

**resistance of 0.5k****. Using
**

**Ohm’s law, and the potential
**

**divider equation: V = 1.736V.
**

**To find the voltage caused by
**

**the 4 V generator, the 6 V
**

**generator is replaced by its
**

**1k**** internal resistance. In
**

**this case: V = 2.315 V.
**

**Now the total voltage in the
**

**original circuit across the
**

**2.2k**** resistor is simply the
**

**sum of these: 4.051 V **

3

*University of Technology
*

*Laser and Optoelectronics Engineering Department
*

*Laser Engineering Branch
*

*Power electronics 2010-2011
*

**3. **Connect the circuit below, when V1 = on and V2 = short

**4. **Measure values of **( I1 , I2 , I3 ) **and record it in the table

I1 (mA) I2 (mA) I3 (mA)

**100**** 82**

**5 V
**

**5
0
**

**9 V
**

**A
**

**I2
**

**A
**

**I1
**

**A I3
**

**100**** 82**

**5 V
**

**5
0
**

**A
**

**I2
**

**A
**

**I1
**

**A I3 **

4

*University of Technology
*

*Laser and Optoelectronics Engineering Department
*

*Laser Engineering Branch
*

*Power electronics 2010-2011
*

**5.** Connect the circuit below, when V1 =short and V2 = on

**5. **Measure values of **( I1 , I2 , I3 ) **and record it in the table

I1 (mA) I2 (mA) I3 (mA)

**6. **From results, calculate the current pass through each resistor and

voltage across each resistor.

**Discussion
1. **Compare between the theoretical and practical results.

**2. **Comment on your results.**
3. **Find ( Ia ) by using superposition theorem for the circuit below**.
**

**100**** 82**

**5
0
**

**
9 V
**

**A
**

**I2
**

**A
**

**I1
**

**A I3 **

5

*University of Technology
*

*Laser and Optoelectronics Engineering Department
*

*Laser Engineering Branch
*

*Power electronics 2010-2011
*