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AC Circuit Problem

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asked Dec 12, 2015 in ELECTRICAL ENGINEERING by anonymous

1 Answer

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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

image

image.

Where image is the resistance at the voltage sources.

And image 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 image.

 

Find the Thevinins equivalent resistance of the circuit.

1.Open the load resistor.

2.Open Current Sources and Short Voltage Sources.

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

Redraw the circuit :

image

Step 2:

Observe the circuit:

image.

image can be written in polar form as image.

image can be written in polar form as image.

Three impedances are in parallel.

image

image.

Step 3:

Observe the circuit:

image can be written in polar form as image.

image.

image.

image can be written in polar form as image.

Substitute corresponding values in the image.

image

image can be written in polar form as image V. 

Solution:

image V.

answered Dec 14, 2015 by cameron Mentor
edited Dec 14, 2015 by cameron

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