The capacitor in the circuit below is charged such that the top plate has a char

Question

The capacitor in the circuit below is charged such that the top plate has a charge +Q0 and the bottom plate -Q0. At time t=0, the switch is closed and the circuit oscillates with a frequency of 500 radians/second.

1)

What is the value of the capacitor C?

C = 1 x 10-3 F

C = 2 x 10-3 F

C = 4 x 10-3 F

2)

Briefly explain your reasoning

3)

Which of the following plots best represents the energy in the inductor as a function of time starting just after the switch is closed?

A

B

C

D

E

4)

5)

When the energy stored in the capacitor reaches its maximum again for the first time after t > 0, how much charge is stored on the top plate of the capacitor?

+Q0

+1/2Q0

0

-1/2Q0

-Q0

6)

Briefly explain your reasoning

Explanation / Answer

Given,

L = 4 x 10^-3 H ; w = 500 rad/s

1)we know that

w = 1/sqrt(LC)

C = 1/w^2 L = 1/(500^2 x 4 x 10^-3) = 1 x 10^-3 F

Hence, C = 1 x 10^-3 F

2)the moment switch is closed, the circuit oscillated with resonance frequency.

3)(D) is the correct graph

4)since, U = 1/2 L I^2

so it cant not go negative in any case

5)-Q

6)the charge on capacitor is maximum when current is zero.

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