Question

A 18.0 uF capacitor and a 5.10 mH inductor are connected in series with an open switch. The capacitor is initially charged to 6.30 uC. What is the angular frequency of the charge oscillations in the capacitor after the switch is closed? Answer should be in rad/s.

Answer 1

Concepts and reason

The concepts used to solve this problem are the angular frequency of the series LC circuit and Resonance.

Initially, explain the formula for the angular frequency of the LC circuit using the concept of resonance and angular frequency and then, use this formula to determine the value of the angular frequency of a seriescircuit.

Fundamentals

Angular frequency:

Angular frequency of a series LC circuit is given as,

Here, is the angular frequency, is the capacitance of the capacitor andis the inductance of the inductor.

Resonance:

Resonance is a condition which is attained as a result of oscillations in a circuit because the stored energy is transferred from the inductor to the capacitor.

The condition of resonance is attained when the capacitive and inductive reactance are equal in magnitude at a particular angular frequency when thecircuit is driven by an external source.

Here, is the inductive reactance andis the capacitive reactance.

This particular frequency at which the resonance occurs is called as the resonant frequency of thecircuit. It is given by the formula:

Angular frequency of a series LC circuit is given as,

Substitute for and for in the above equation,

Hence, the angular frequency is.

Ans:

The angular frequency is.