Millman theorems is a circuit analysis theorem that is used to solve parallel voltage sources in circuit. In Millman’s theorem the multiple voltage containinting resistances in respective branches can be reduced.

Consider the circuit shown below:

Using Millman’s theorem we can reduce the above circuit to a single voltage source and a series resistor:

Where R_eq:

And V_eq:

Let’s solve an example to better understand this:


Find the equivalent circuit for load resistor, and find the current supplied to load.

Solution:

Using the above formula:

Req = 2.72 ohms … (Learn How to solve parallel resistors)

Veq = 6.27 V … (Learn Ohm’s Law)

From above we have finally:

Current supplied to load:

I_L = V / (R_eq + R_l) = 6.27 V / 5.72 ohms = 1.09 A