A 4.5 µF capacitor is connected to a 15.0 V battery and becomes fully charged. I

Question

A 4.5 µF capacitor is connected to a 15.0 V battery and becomes fully charged. It is then disconnected from the battery and connected to a 6.5 mH inductor as shown

(a) How much charge is on the capacitor when it is fully charged?

(b) The final LC circuit begins to oscillate. What is the frequency of the oscillations?

(c) Write down an expression for q(t), the charge on the capacitor as a function of time.

(d) What is the maximum current through the inductor?

(e) When the current is half the maximum value, how much energy is stored in the capacitor and how much energy is stored in the inductor?

Explanation / Answer

a)

charge on the capacitor , Q = C * V

Q = 4.5 *10^-6 * 15

Q = 6.75 *10^-5 C

the charge on the capacitor is 6.75 *10^-5 C

b)

oscillation frequency = 1/(2pi * sqrt(L * C))

oscillation frequency = 1/(2pi * 4.5 *10^-6 * 0.0065)

oscillation frequency = 930.8 Hz

the oscillation frequency is 930.8 Hz

part c)

for the charge as a function of time

Q = Qo * cos(2 * pi * f * t)

Q = 6.75 *10^-5 * cos(2 * pi * 930.8 * t )

Q = 6.75 *10^-5 * cos(5847.05 * t) C

the charge on the capacitor is 6.75 *10^-5 * cos(5847.05 * t) C

part d)

for the maximum current ,

energy stored in inductor = maximum energy stored in capacitor

0.5 * 4.5 *10^-6 * 15^2 = 0.5 * 0.0065 * I^2

solving for I

I = 0.394 A

the maximum current in the inductor is 0.394 A

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