Experiment # 5: **The Superposition Theorem.**

** Objective**: To study and verify the Superposition theorem.

** Prelab**: In the circuit of figure 5.1 use Superposition theorem to find voltage V.

** Theory**: The principle of superposition provides us with the ability to reduce a complicated circuit with several sources to several simpler circuits – each containing only a single independent source. Formally, it may be stated as:

For any linear circuit containing multiple independent sources, the current or voltages at any point in the network may be calculated as the algebraic sum of the individual contributions of each source acting alone.

To determine the contribution due to an independent source, all other independent voltage sources are made zero by short-circuiting them, and all other independent current sources are made zero by open-circuiting them; however, dependent sources are not reduced to zero and remain in the circuit.

Superposition is a fundamental property of linear equations and therefore can be applied to any linear effect. Superposition does not hold (in general) for nonlinear relationships (e.g. power); thus, we cannot determine the power dissipated in each circuit element from the individual powers.

** Procedure**:

- Connect the circuit shown in figure 5.1
- Measure the voltage v across R3.
- Remove the 20 volt source, replace it with a short circuit and measure the voltage across R3.
- Put the 20 volt source back into the circuit. Then remove the 10 volt source, replace it with a short circuit and measure the voltage across R3.

** Results**:

- The voltage across R3 as measured in part 3 of the procedure plus the voltage measured across R3 in part 4 of the procedure should equal the voltage measured across R3 in part 2 of the procedure.
- Analyze the circuit using either mesh or nodal analysis and verify the above results.
- Perform a PSPICE analysis of figure 5.1 and check your results.

Experiment # 5: **The Superposition Theorem.**