An l-c circuit containing an 82.0-mh inductor and a 1.60-nf capacitor oscillates with a maximum current of 0.800 a . assuming the capacitor had its maximum charge at time t= 0, calculate the energy stored in the inductor after 2.40 ms of oscillation.

19.5 mJ

Explanation:

Assuming perfect components without resistance or losses, the circuit should oscillate indefinetly.

The circuit will have a natural pulsation of

So, by the time t = 2.4 ms, 333.33 cycles would have passed

Therefore it would be at one third after the beginning of the cycle. The circuit would be in an equivalent state as t = (7.2 us)/3 = 2.4us

At t=0 the capacitor is fully charged, so the voltage is maximum and the current is 0. The current will increase towards a maximum of 800 mA at t=T/4, then decreas to 0 at t=T/2, decrease to -800 mA at 3T/4 and go back to 0 at t=T following a sine wave.

The equation of this sine wave would be

Since w = 2π/T

w * T = 2π

The current stored in an inductor is

the part of the wave he is travelling on is the crest