In the given circuit, initially switch S1 is closed, and S2 and S3 are open. After charging of capacitor, at t=0,S1 is opened and S2 and S3 are closed. If the relation between inductance, capacitance and resistance is L=4CR2, then find the time (in s) after which current passing through capacitor and inductor will be same (given R=ln2mΩ,L=2mH):
Current through
S2 loop is ε2Re−t2CR
current through S3 loop is ε2R(1−e−tL/2R)
⇒e−t2CR=1−e−tL/2R
⇒e−t2CR=1−e−t4CR2/2R
⇒2e−t2CR=1
⇒e−t2CR=1/2
⇒−t2CR=ln(1/2)
⇒t=2CRln(2)=L2Rln(2)=1s