AC Circuit Problem

Step 1:

Millman's theorem:

Millman's theorem is applicable to a circuit which may contain only voltage sources in parallel or a mixture of voltage and current sources connected in parallel.

This theorem is nothing but a combination of Thevenins Theorem and Nortons Theorem.

Millman states that the voltage at the ends of the circuit is given by

.

Where is the resistance at the voltage sources.

And is the resistance on the branch with no source or generators.

For our circuit,

voltage at the end of the nodes A and B is .

Find the Thevinins equivalent resistance of the circuit.

2.Open Current Sources and Short Voltage Sources.

3.Calculate the Open Circuit Resistance. This is the Thevenin Resistance (RTH).

Redraw the circuit :

Step 2:

Observe the circuit:

.

can be written in polar form as .

can be written in polar form as .

Three impedances are in parallel.

.

Step 3:

Observe the circuit:

can be written in polar form as .

.

.

can be written in polar form as .

Substitute corresponding values in the .

can be written in polar form as  V.

Solution:

V.