An L-C circuit consists of an inductor with an inductance of 55.0 mH and a capac

Question

An L-C circuit consists of an inductor with an inductance of 55.0 mH and a capacitor with a capacitance of 200 F . The initial charge on the capacitor is 6.00 C , and the initial current in the inductor is zero.

Part A

What is the maximum voltage across the capacitor?

Part B

What is the maximum current in the inductor?

Part C

What is the maximum energy stored in the inductor?

Part D

When the current in the inductor has half its maximum value, what is the charge on the capacitor?

Part E

When the current in the inductor has half its maximum value, what is the energy stored in the inductor?

Explanation / Answer

(A) V = Q / C = (6uC) / (200 uF ) = 0.03 V

(B) C V^2 / 2 = L I^2 / 2

(6 x 10^-6) (0.03^2) = (0.055) I^2

I = 3.13 x 10^-4 A

(C) Umax = C V^2 /2 = 2.7 x 10^-9 J  

(D) 2.7 x 10^-9 = 0.055 (3.13 x 10^-4/ 2)^2 / 2 + Q^2 / 2C

Q = 0.9 x 10^-6 C = 0.09 uC

(E) U = Umax / 4 = 0.675 x 10^-9 J

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