superposition theorem

The superposition theorem for electrical circuits 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. 

the contribution of each individual source, all of the other sources first must be set to zero by

• Replacing all other independent voltage sources with a short circuit
• Replacing all other independent current sources with an open circuit 

       

Suppose there are two voltage source s V₁ and V₂ acting simultaneously on the circuit. Because of these two voltage sources, say current I flows through the resistance R.Now replace V₂ by short circuit, keeping V₁ at its position and measure current through the resistance, R. Say it is I₁.Then replace, V₁ by short circuit, reconnect V₂ to its original position and measure current through the same resistance R and say it is I₂.Now if we add these two currents, I₁ and I₂ we will get the current which is equal to the current - was actually flowing through R, when both voltage source s V₁ and V₂ were acting on the circuit simultaneously. That is I₁ + I₂ = I.