Use the Superposition theorem to find V0 in the circuit Solu

Use the Superposition theorem to find V_0 in the circuit.

Solution

By using superposition theorem first we will make

Current source active

Voltage source make it zero i.e short

Now find Vo due to current source Vo(current)

as 2k and 1k in series equvalent resistance Req=2+1=3k, now 3k is in parallel with 6k as voltage source is shorted

Total resistance =Rt= Req parllel 6k=Req*6k/(Req+6k)=18/9=2k

Vo(current)=I*Rt=2m *2k=4 V

Now make

Voltage source active

current source make it zero i.e open

Now 6k and 2k and 1 k in series Rt=6k+1k+2k=9k

Vo(voltage)=V*6K/9k (voltage division) 3*6/9= 2V

Vo(voltage)=2 V

By superposition theorem Vo=Vo(voltage)+Vo(current)=2+4=6 V

so Vo=6 V