Millman’s theorem for AC network states that *if there as “n” number of voltage sources having magnitude V _{1}, V_{2}, V_{3},…..V_{n} hving internal magnitude Z_{1}, Z_{2}, Z_{3},…..Z_{n} respectively, then these sources may be replaced by a single voltage source V_{m} having equivalent series internal impedance Z_{m} given by the equations*

…..(1)

And …..(2)

Where Y_{1}, Y_{2},…..Y_{n} are the admittances corresponding to impedance Z_{1}, Z_{2}, Z_{3 }…..,Z_{n} (figure 1)

Let us see an example of Millman’s theorem

**Example 1. Using Millman’s theorem find the current in the load Z _{L} in figure 2.**

Solution, Since Millman’s theorem is applicable only to voltage source hence, the current source in the given circuit is converted to voltage source first as shown in figure 3.

As per Millman’s theorem, the equivalent voltage source is given by.

Therefore,