Find the circuit time constant in the expression of v0t for

Find the circuit time constant in the expression of v_0(t) for 0. 3 sec 6 sec 12 sec 24 sec

Solution

here when switch is closed 4ohms resistor (series)is neglected.

4ohms with voltage va drop is considered and the dependent source has the resistance equivalent to twice that of 4ohms i.e 8ohms..

Req=> 4+8= 12 and C=2F

time constant= Req*C= 24sec