Question

An 8.5 nF capacitor is charged up by a 20 V battery. The battery is removed and replaced with a coil of wire. It then takes 7.3 x 10-5 s for this now LC circuit to undergo a full charging cycle. (a) Calculate the inductance of the coil

(b) Calculate the total energy of the circuit

(c) Calculate the charge on the capacitor after 1 x 10-5 s.

Answer 1

Given:

C = 8.5 nF

V = 20 V (by battery)

Initially the capacitor is charged up by the battery, then it is removed. Then it is connected across an inductor.

Let the inductance of inductor be L.

Time period of LC oscillation =

a) The time period of LC oscillation is given by

[answer]

b) Total energy of circuit remains constant, and it is equal to initial energy of capacitor.

Energy in the capacitor = [answer]

c) The charge is oscillating in the LC circuit.

and at t=0, the capacitor is fully charged.

Therefore, the equation of oscillating charge can be written as

[where = angular frequency, Q = initial charge]

Now, Q = CV = 8.5*20 = 170 nC and

.

Therefore,

=110.82nC [answer]