# Superposition Theorem – Explanation – Solved Example Electrical B.Tech.

## Superposition Theorem

According to Superposition theorem, if there are a number of e.m.f.s, acting simultaneously in any linear bilateral network, then each e.m.f acts independently of the others i.e. as if the other e.m.f.s, did not exist. The value of current in any conductor is the algebraic sum of the currents due to each e.m.f Similarly, voltage across any conductor is the algebraic sum of the voltages with each e.m.f. would have produced while acting singly. In other words, current in or voltage across, any conductor of the network is obtained by superimposing the currents and voltages due to each e.m.f. in the network. It is important to keep in mind that this theorem is applicable only to linear networks where current is linearly related to voltage as per Ohm’s law.

### Superposition Theorem may be stated as follows :

Hence, this theorem may be stated as follows :-

“In a network of linear resistances containing more than one generator (or source of e.m.f.), the current which flows at any point is the sum of all the currents which would flow at that point, if each generator were considered separately and all the other generators replaced for the time-being by resistances equal to their internal resistances”.

#### Explanation Superposition Theorem

Explanation: In fig. 1(a), and I represent the values of currents which are due to the simultaneous action of the two sources of e.m.f. in the network. In figs 1 (b) the current values are shown which would have been obtained if left-hand side battery had acted alone. Similarly, fig. 2 represents conditions obtained when Right-hand side battery acts alone. By combining the current values of fig. 1(b) and fig. 2 the actual values of fig.1 (a) can be obtained.

(Addition if direction of current is same and subtraction if direction of current is opposite)

## Example of Superposition Theorem

Solved Example | numerical of superposition theorem

ELECTRIC CIRCUITS TOPIC