In a certain oscillating LCcircuit, the total energy is converted from electrical energy in the capacitor to magnetic energy in the inductor in 1.61 μs. What are (a) the period of oscillation in microseconds and (b) the frequency of oscillation? (c) How long after the magnetic energy is a maximum will it be a maximum again?

a) 6.44 us

b) 155 kHz

c) 3.22 us

Explanation:

In an oscillating LC circuit the energy flows from capacitor to inductor back and forth. The capacitor is fully charged when the voltage peaks, it does this twice per cycle, in opposite polarities (positive and negative voltage peaks). During these peaks the current is zero, so the energy stored in the inductor is zero. During a cycle the voltage crosses zero twice (once going up and once going down), during these moments the current is maximum, in different directions, and in those moments the inductor is charged at maximum. The time between the voltage peak (cap fully charged, inductor empty) and the voltage crossing zero (cap empty, inductor full) is 1/4 of the cycle period.

Since we know this time to be 1.6 us, we know the period must be 4*1.61 us = 6.44 us.

The frequency is 1/T = 1 / 6.44e-6 = 1.55e5 = 155 kHz

The magnetic energy maximums happen when the voltage crosses the zero, this happens every T/2 = 3.22 us.