DC NETWORK THEOREMS – PART – 09 – SUBSTITUTION THEOREM

This theorem is based upon substitution of one element by another equivalent element.

Substitution theorem can be used in both linear and nonlinear circuits. This theorem is used to prove several other theorems.

SUBSTITUTION THEOREM

Any branch or network can be replaced by a different branch as long as its potential and current remain unchanged. When the original branch is passive, either a voltage source or a current source is generally used for the substituted branch.

                                                 [OR]

A known voltage to a circuit can be replaced by an ideal voltage source and known current can be replaced by an ideal current source. A resistance R carrying a current I has a voltage drop of IR. Then according to this theorem, this resistor can be replaced by a compensation e.m.f equal to IR. Similarly if the voltage across an element R is V, the element can be replaced by a current source 
I = V/R. No other part of the network is affected by this substitution.

LIMITATIONS

This theorem cannot be applied unless the solution is already known.

APPLICATIONS

This theorem can be applied to any linear, nonlinear, time varying and time invariant.

This theorem is applicable to both time domain and S domain.

This theorem is useful in analyzing the behavior of the network.