AC Effective Voltage

Question

Answer 1

Step 1:

Use Superposition principle to calculate voltage across the resistor .

Super Position Theorem :

Take one current source at a time and replace all other with voltage with short or internal resistance and current sources with open.

The current flowing in the circuit is .

 in polar form can be written as .

 in complex form can be written as .

Apply current divider rule: .

Find the total impedance .

is in series with .

is in series with .

is in parallel to .

is in series with , and .

Current division rule:

Find the voltage drop across the resistor .

 V.

Step 2:

Take one voltage source at a time and replace all other with voltage with short or internal resistance and current sources with open.

The voltage in the circuit is .

 in polar form can be written as .

in complex form can be written as .

Apply KVL to loop 1:

Find the voltage drop across the impedance .

 V.

Step 3:

By superposition principle : 

The Voltage across the resistor is .

Voltage across the resistor is 

Solution:

Voltage across the resistor is