Energy Storage in an L-C Circuit?

Question

An L-C circuit has an inductance of 0.370 H and a capacitance of 0.240 nF. During the current oscillations, the maximum current in the inductor is 1.00 A.

for the first one i got .74 but that was incorrect

What is the maximum energy E_max stored in the capacitor at any time during the current oscillations? in joules

How many times per second does the capacitor contain the amount of energy found in part A? in times per second

Answer 1

The energy stored in an inductor is 0.5*L*I^2.  So the maximum energy is 0.185 J.  The circuit will oscillate at a frequency of w = √[1/(L*C)] = 106*10^3 rad/sec.  The current in the circuit at any time t is

I = (1.0)*sin(w*t)

The voltage across the inductor is then L*w*cos(w*t).  The peak voltage is then Vp = 39.2*10^3 volts.  

The voltage across the capacitor is the same as the voltage across the inductor, so V = 39.2*10^3*cos(w*t)

The energy in the capacitor is 0.5*C*V^2, = 0.185*cos^2(w*t) J.   (As expected, the peak energy is the same as the peak energy in the inductor.)

The capacitor reaches peak voltage twice during one cycle.  There are w/(2π) cycles per second, so the capacitor stores the peak energy w/π times per second, 33.7*10^3 times per sec