## Objective: Verification of Millman's Theorem

This theorem is a combination of Thevenin's and Norton's theorems. When a number of voltage source (V_{1},V_{2},...,V_{n}) are in parallel having internal resistances (R_{1},R_{2},...,R_{n}) respectively, the arrangement can be replaced by a single equivalent voltage source V in series with an equivalent series resistance R as given below Fig. 1 and Fig 2.

Fig.1. A number of voltage source fading power to a load.

Fig. 2. Equivalent voltage and resistance of the source network following millman theorem.

As per Millman's Theorem ,

This voltage represents the thevenin's voltage V. The resistance R can be found , as usual , by replacing each voltage source by a short circuit. If there is a load resistance R_{L} across the terminals A and B , then the load current I_{L} is given by