Consider the circuit shown below with the following parameters:
I_(S)=0.5A,
L=18H,
C=(1)/(60)F,
R_(1)=9\Omega ,
R_(2)=7\Omega .
The switch in this circuit has remained open for a long time before it is closed at t=0. Analyse the circuit and show that for t>0, the indicated voltage response has the
form
v(t)=K_(1)e^(-\lambda _(1)t)+K_(2)e^(-\lambda _(2)t)V,
for some constants K_(1),K_(2),\lambda _(1), and \lambda _(2), where \lambda _(1)<\lambda _(2). Hence, determine the value of the constant K_(1) (in V ) in the response.
Answer