AC Impedance Current

Question

Answer 1

Step 1:

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 the given circuit,

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

 

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 (R_TH).

Redraw the circuit:

Step 2:

Observe the circuit:

can be written in complex form as .

can be written in complex form as .

can be written in complex form as .

can be written in complex form as .

Three impedances are in parallel.

.

Step 3:

Observe the circuit:

can be written in complex form as .

.

can be written in complex form as .

.

can be written in complex form as .

Substitute corresponding values in the millman's formula.

 can be written in polar form as .

Voltage passes through each branch is .

Find the current passes resistor .

.

Solution:

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