In an ideal LC circuit the resistance is 0 and there is no energy dissipation. A
ID: 1465923 • Letter: I
Question
In an ideal LC circuit the resistance is 0 and there is no energy dissipation. A 6.00F capacitor is charged fully by a 12V DC battery. This capacitor is connected to an inductor of inductance L= 25mH.
a. Calculate the angular frequency, , the frequency, f and the period of the oscillation, T.
b. For the above LC circuit determine the initial charge on the capacitor, Q0, and the maximum current Imax in the circuit.
c. Calculate the maximum energy stored in the capacitor and the maximum energy stored in the magnetic field of the inductor.
Explanation / Answer
a)
w = 1/sqrt(LC)
w = 1/sqrt(25*10^-3*6*10^-6) = 2582 rad/s
f = w/(2*pi) = 2582/(2*pi) = 411 Hz
T = 1/f = 0.0024 s
(b)
Qo = C*V = 6*10^-6*12 = 72*10^-6 C
Imax = V^2/R = V/sqrt(L/C) = 12/sqrt(25*10^-3/(6*10^-6)) = 0.185 A
(c)
Ec = 0.5*C*V^2 = 0.5*6*10^-6*12^2 = 0.000432 J
EL = 0.5*L*I^2 = 0.5*25*10^-3*0.185^2 = 4.3*10^-4 J
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