Question

An LC circuit is built with a 10 mH inductor and an 12.0 pF capacitor. The capacitor voltage has its maximum value of 40 V at t=0s.

Part A

How long is it until the capacitor is first fully discharged?

Express your answer with the appropriate units. (t=?)

Part B

What is the inductor current at that time?

Express your answer with the appropriate units.(I=?)

Answer 1

Inductance L = 10 mH = 10 x10 -3 H

Capacitance C = 12 x10 -12 F

Maximum voltage Vo = 40 volt

(A). Required time t =?

Charge on capacitor q = Q cos wt              ------------( 1)

Where Q = maximum charge = CVo

               = (12 pF)(40) = 480 pcoulomb = 480x10 ^-12 coulomb

            w = angular frequency = 1/[LC]

               = 1/[10 x10 ^-3 x 480 x10 ^-12 ]

               = 1/(21.9 x10 ^-5)

               = 4.564 x10 ³ rad/s

From equation(1) , q = Q cos wt

                           CV = CVo cos wt

                              V = Vo cos wt

V = 0 when t= t

   0 = Vo cos wt

    0 = cos wt

wt = /2

   t = /2w

     = 3.1415 /(2x 4.564 x10 ³ )

     = 3.441 x10 ^-4 s

(B).Current in the inductor at that time io =maximum value

                                                           = Qw= 480x10 ^-12 x 4.564 x10 ³

                                                            = 2.19x10 ^-6 A