6.0. An LC circuit has an inductance of 2.81 mH and a capacitance of 9 pF (Fig.
ID: 1383617 • Letter: 6
Question
6.0. An LC circuit has an inductance of 2.81 mH and a capacitance of 9 pF (Fig. 32.15). The capacitor is initially charged with a 12-V battery when the switch S1 is open and switch S2 is closed. S1 is then closed at the same instant that S2 is opened so that the capacitor is shorted across the inductor. (a) Find the frequency of oscillation. (b) What are the maximum values of charge on the capacitor and current in the circuit? (c) Determine the charge and current as functions of time. (d) What is the total energy stored in the circuit?Explanation / Answer
a) f = 1/(2*pi*sqrt(L*C))
= 1/(2*pi*sqrt(2.81*10^-3*9*10^-12))
= 1*10^6 Hz
b) Qmax = C*V
= 9*12
= 108 pC or 1.08*10^-10 C
c)
d) U = Q^2/(2*C)
= (108*10^-12)^2/(2*9*10^-12)
= 6.48*10^-10 J or 648 pJ
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