Question

An LC circuit has an inductor with inductance 0.05 H and a capacitor with capacitance 5 μF. All of the energy is stored in the capacitor at t=0, and the total charge is 3×10-5 C. (a) What is the angular frequency of the oscillations in this circuit? (b) Find a mathematic equation for q(t). (c) What is the maximum current flow through the circuit? (d) How long does it take the capacitor to become completely discharged?

Answer 1

Given inductance L = 0.05 H and capacitance C = 5 μF.

1.

The angular frequency of the oscillations

2.

The capacitor is completely charged at t=0.

So q(0) = =

from (1)

q(t) =

= () cos (​​​​​​)

3.

The current is maximum when all the energy is stored in the Inductor. From the Law of Energy Conservation

= ​​​​ *

=

4.

​​​​​​The Capacitor becomes completely discharge in one fourth of a cycle or during a time T/4, where T is the period of the oscillations.

= s

=

The time taken for capacitor to become fully charged

T/4 =

=