For the electric circuit shown in the figure beow suppose th

For the electric circuit shown in the figure beow, suppose that a surge has caused an initial charge Q0 C to be deposited on the capacitor. The circuit is closed, but otherwise dead. Suppose C=0.1 faradays L=2 henries and R=0.01 ohms. How long will it take for the charge Q to be always less than 0.01 Q0??

the answer is 30.7 min

Could anybody possibly help me with the question...? work plz...

as Models and in Science En Dierential Equations +Q It is an Fig. 1.16 The LCR circuit. TY Yny 11 N N1

Solution

In a RLC circuit ,charge as a function of time is given by

Q=Q_oe^-Rt/2L

0.01Q_o=Q_oe^-0.01t/2*2

-(2.5*10^-3)t =Ln(0.01) =-4.605

t=1842 seconds

in minutes

t=1842/60 =30.7 minutes