(1)

Step 1:

Find the Thevinins equivalent resistance.

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:

All the four impedances are in series.

can be written in complex form as .

can be written in complex form as .

can be written in polar form as

Solution:

.

.

is in series with .

is in series with .

and are in parallel.

in polar form can be written as .

Solution:

(2)

Step 1:

Find the thevinins equivalent voltage.

1.Open the load resistor.

2.Calculate the Open Circuit Voltage. This is the Thevenin Voltage (V_TH).

Use Superposition principle to calculate volatge across A and B.

Find the current through .

Super Position Theorem :

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

in complex form can be written as .

Current in the circuit is .

Current in the circuit is

Voltage drop acoss : .

Step 2:

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

in complex form can be written as .

Current in the circuit is .

Current in the circuit is

Voltage drop acoss : .

Step 3:

By superposition principle : 

The Voltage acoss the terminal A and B is .

Thevinins equivalent voltage is 

Solution: