In anoscillating LC circuit, L = 20.0 mHand C = 7.80 µF. At time t = 0the curren

Question

In anoscillating LC circuit, L = 20.0 mHand C = 7.80 µF. At time t = 0the current is 9.20 mA, thecharge on the capacitor is 3.50 µC, and the capacitor is charging. (a) What is the total energy in the circuit?
J
(b) What is the maximum charge on the capacitor?
C
(c) What is the maximum current?
A
(d) If the charge on the capacitor is givenby q = Q cos(t + ?),what is the phase angle ??
°
(e) Suppose the data are the same, except that the capacitor isdischarging at t = 0. What thenis ??
° (a) What is the total energy in the circuit?
J
(b) What is the maximum charge on the capacitor?
C
(c) What is the maximum current?
A
(d) If the charge on the capacitor is givenby q = Q cos(t + ?),what is the phase angle ??
°
(e) Suppose the data are the same, except that the capacitor isdischarging at t = 0. What thenis ??
°

Explanation / Answer

L = 20.0 mH,C = 7.80 µF.at t = 0, i = 9.20 mA,q = 3.50 µC, a) E = Li2/2 + q2/(2C) = 1.63*10-6J b) E = Q2/(2C), so Q = (2CE) = 5.05 C c) E = LI2/2, so I = (2E/L) = 12.77 mA d)q = Q cos(t + ),i = dq/dt = -Qsin(t + ) t = 0, q = Qcos, i = -Qsin cos = q/Q, sin = -i/(Q) < 0 = -0.805 rad e) discharging, i = dq/dt < 0, sin > 0 = +0.805 rad

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