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Superposition Theorem

If there are several sources of e.m.fs. acting simultaneously in an electric circuit, then according to this theorem e.m.f. of each source acts independently of those of other sources i.e. as if the other sources of e.m.f, did not exist and current in any branch or conductor of a network is equal to the algebraic sum of the currents due to each source of e.m.f.separately, all other e.m.fs. being taken equal to zero. This theorem is applicable only in linear circuits i.e. circuits consisting of resistances or impedances in which Ohm’s law is valid, in circuits having non-linear impedances such as thermionic valves and metal rectifler,this theorem is not applicable. However, Superposition theorem can be applied to a circuit containing current sources and even to circuits containing both voltage sources and current sources. To remove a current source from the circuit, circuit of the source is opened leaving in place any conductance that may be in parallel with it, just as series resistance is kept in place when voltage source is removed.

The above theorem is applied when we are to determine the current in any particular branch of a network containing several voltage sources or current sources or both voltage sources and current sources. Though the application of this theorem requires a little more work than other methods such as the circulating current method but it avoids the solution of two or more simultaneous equations. After a little practice with this method, equations can be written directly form the original circuit diagram and labour in drawing extra diagram is saved.

The super position theorem can be stated as below:

In a liner resistive network containing two or more voltage sources, the current through any element (resistance or source) may be determined by adding together algebraically the currents produced by each source dating alone, when all other voltage sources are replaced by their internal resistances. If a voltage source has no internal resistance, the terminal to which it was connected are joined together. If there are current sources present they are removed and the network terminals to which they were connected are left open.

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