Super position Theorem

Statement

Super position Theorem states that the voltage across (or current through) an element in a linear circuit is equal to the algebraic sum of voltages across (or currents through) that element due to each independent source acting alone.

Alternatively it can be explained as; in a circuit having multiple number of sources, which are turned on simultaneously. The response (voltage or current) obtained
at an element under such condition will be equal to the sum of the responses obtained when each source is acting one at a time.

The superposition theorem is applicable only to linear parameters and it is not applicable to non linear quantities. It can be applied for finding the voltage and current but cannot applied for measuring power.

Solving a circuit using superposition theorem

Consider the following circuit as having two sources, one current source and one voltage source.

Main circuit to be solved using superposition theorem

To find the voltage V₀ across the resistor R₂ using superposition theorem, first turn ON only one source. For example, turn ON voltage source and turn off all other sources i.e. the current source in this circuit is turned OFF. It gives the following circuit. Find the voltage across the resistor R₂ and let this be V’.

Circuit when source V is acting alone

Now turn ON only the current source and turn OFF all other sources. Here the voltage source is turned OFF as shown by the below circuit. Find the voltage across the resistor from the obtained circuit and let this be V’’.

Circuit when source I is acting alone

Adding V’ and V’’ will get the actual value of the voltage V₀ when both the sources are turned on as in the first circuit i.e. V=V’+V’’.