Superposition Theorem

So far we have used mesh analysis for voltage sources and nodal analysis for current sources. What if a circuit contains both of them? In such a case, you can either use a mdified version of mesh/nodal analysis or you can adopt a different approach namely that of superposition theorem. This simple theorem allows you to consider the effect of a single energy source and a time and then to sum up the individual responses to get the complete response. The statement is given below

In a linear network containing two or more energy sources, the response is given by the sum of the responses with sone source acting at a time while the rest are suppresed.

A voltage source is suppresed by shorting it while a current source is suppressed by opening it. While calculating the sum, be particular about the directions of the currents and voltages since you have to take the algebraic sum. One drawback of the superposition theorem is that it can't be applied to powers.

In the example circuit, we will calculate the current through the resistance R using superposition theorem.

Example

Enter the values of the circuit elements
V: I1: R1: R2: R:

The results are given below:

Current due to V downwards:

Current due to I1 downwards:

Total Current downwards: