Obtain the Thevenin equivalent circuit parameters V_th and R_th for the following network.

Concept:

According to Thevenin’s theorem, any linear circuit across a load can be replaced by an equivalent circuit consisting of a voltage source Vth in series with a resistor Rth as shown:

Vth = Open circuit Voltage at a – b (by removing the load), i.e.

R_th = equivalent resistance obtaining by deactivating sources.(Independent voltage source is short-circuited

and Independent current source is open  circuited)

Calculation:

Calculation of V_th

Apply KVL in the loop

20 - 3I - 6I + 10 = 0

I = (20 + 10) / (3 + 6)

I = 30 / 9

V_6Ω  = (30 / 9) × 6 

V6Ω = 20 V

Now apply KVL in the outer loop

- 10 + V_6Ω  - V_ab = 0

V_ab = V_th = (20 - 10) V = 10 V

where, I = current through loop 

Calculation of R_th

R_th = [3 || 6] + 3

Rth = 2 + 3 = 5 Ω