Thevinin equivalent

Question

Answer 1

(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 :

The two networks are similar and they are in series to each other.

Step 2:

Convert the delta network to star network.

Resistors R_a and R_b are in parallel.

Resultant R_t is in series with R_c.

R_eq1 = 1+ 4 = 5 .

Similarly for the second network , R_eq2 = 5 .

So the equivalent resistance will be R_th = 5 + 5 = 10 .

Solution :

Thevenin Resistance is R_th = 10 .

Answer 2

(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).

Redraw the circuit :

 

The netwrok has two independent loops.

Find the current in each loop.

Loop 1:

Voltage at node A  :

Step 2:

Loop 2:

Voltage at node B  :

Step 3:

Find Thevenin Voltage (V_TH).

Thevenin Voltage V_TH  = V_A + V_B .

V_TH  = -2 - 6

V_TH  = -8 V.

Therefore Thevenin Voltage V_TH  = - 8 V.

Solution :

Thevenin Voltage is V_TH  = - 8 V.