An LC circuit like the one shown in Figure 32.16 contains an 95.0 mH inductor an
ID: 1796127 • Letter: A
Question
An LC circuit like the one shown in Figure 32.16 contains an 95.0 mH inductor and a 12.0 µF capacitor that initially carries a 170 µC charge. The switch is open for t < 0 and then closed at t = 0.
(a) Find the frequency (in hertz) of the resulting oscillations.
149.06 Hz
(b) At t = 1.00 ms, find the charge on the capacitor.
169.9
Your response differs from the correct answer by more than 10%. Double check your calculations. µC
(c) What is the current in the circuit?
-153.08
Your response differs from the correct answer by more than 10%. Double check your calculations. mA
I got part B and C wrong.
Explanation / Answer
the charge changes as q = Qmax*cos(wt)
Q max = 170 uC
w = 2*pi*f = 2*pi*149.06 Hz
at time t = 1 ms
q = 170*cos(2*pi*149.06*10^-3)
q = 100.7 uC
===============
at any time total energy is constant
Etot = (1/2)*L*I^2 + (1/2)*q^2/C
(1/2)*Qmax^2/C = (1/2)*L*I^2 + (1/2)*q^2/C
Qmax^2/C = LI^2 + q^2/C
(170*10^-6)^2/(12*10^-6) = (0.095*I^2) + (100.7*10^-6)^2/(12*10^-6)
current I = 0.128 A
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