help solving q1

Question

 

1. Use the superposition method to calculate the current flowing through RL in the diagram shown below1. Use the superposition method to calculate the current flowing through RL in the diagram shown below

Answer 1

Step 1:

Find the current through 8 resistor :

Super Position Theorem :

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

Indicate the direction of current in the above circuit.

Equivalent resistance :

6 resistor is in parallel with 8 resistor.

Resistance R_T is in series with 4 resistor.

Step 2:

Circuit current :

Current across each resistor :

Current through 4 resistor is .

Current through load 8 resistor is 0.2884 A.

Current through 6 resistor is 0.3846 A.

Answer 2

Contd..

Step 3:

Now Short circuit the second voltage source.

Indicate the direction of current in the above circuit.

Equivalent resistance :

4 resistor is in parallel with 8 resistor.

Resistance R_T is in series with 6 resistor.

Step 4:

Circuit current :

Current across each resistor :

Current through 6 resistor is

Current through Load 8 resistor is 0.2692 A.

Current through 4 resistor is 0.5384 A.

Step 5:

Current through Load resistor 8 =

             = Current produced by 8 resistor due to 5 V + Current produced by 100 resistor due to 7V

             =0.2884+0.2692

             = 0.5576

Current through 8 resistor is 0.5576 A.

Solution:

Current through 8 resistor is 0.5576 A.