Superposition Theorem

The superposition theorem for electrical circuit states that for a linear system the response (voltage or current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, where all the other independent sources are replaced by their internal impedances.

Example:

 Find R2;

The figure has two(2) voltage source, in order to get the voltage across R2, we need to get first the voltage that being supplied on the other loop by deactivating/turning off the other source.

As you can see, the B2 is already turned off, therefore we can solve it using the voltage division principle.
-The Voltage division can be seen on the past blog for more information!

After that, the B1 must be turned off and B2 is now on in order to get the voltage on the other loop.

 

 I'm sure, we can get now the total voltage that R2 have.

To ascertain the contribution of each individual source, all of the other sources first must be "turned off" (set to zero) by:

1. Replacing all other independent voltage sources with a short circuit (thereby eliminating difference of potential i.e. V=0; internal impedance of ideal voltage source is zero (short circuit)).
2. Replacing all other independent current sources with an open circuit (thereby eliminating current i.e. I=0; internal impedance of ideal current source is infinite (open circuit)).