Question

The switch in the figure below is connected to position a for a long time interval. At t = 0, the switch is thrown to position b. After this time, what are the following? (Let C = 1.30 µF.)

(a) the frequency of oscillation of the LC circuit
Hz

(b) the maximum charge that appears on the capacitor
µC

(c) the maximum current in the inductor
mA

(d) the total energy the circuit possesses at t = 3.00 s
µJ

Answer 1

Concepts and reason

The concept used to solve this problem is LC circuit.

In LC parallel circuit, an inductor and a capacitor are connected in parallel.

At t=0 the switch is connected only to inductor and capacitor. Hence it is a LC circuit.

Use the expression for frequency of LC circuit in terms of capacitance and inductance to find the frequency of oscillation of LC circuit.

Then use the expression for maximum charge in the capacitor in terms of capacitance and voltage to find the expression for maximum charge on the capacitor.

Then find current through the inductor and maximum energy stored in the inductor.

Fundamentals

Expression for the resonance frequency of the LC circuit is,

Here, is the resonance frequency, is the capacitance of the capacitor, and is the inductance of the inductor.

Expression for maximum charge on the capacitor is,

Here, is the maximum charge on the capacitor and is the maximum voltage.

Expression for the maximum current through the inductor is,

Here, is the maximum current and is the angular frequency.

Expression for angular frequency is,

The expression for the total energy stored in the inductor is,

Here, is the total energy stored in the inductor.

(a)

Expression for the resonance frequency of the LC circuit is,

Substitute for , for , and for .

Therefore, the frequency of oscillation of LC circuit is .

(b)

Expression for maximum charge on the capacitor is,

Substitute for and for .

Therefore, the maximum charge on the capacitor is.

(c)

Expression for angular frequency is,

Substitute for and for .

Expression for the maximum current through the inductor is,

Substitute for and for .

Therefore, the maximum current through the inductor is .

(d)

The expression for the total energy stored in the inductor is,

Substitute for and for .

Therefore, the total energy possessed by the circuit at is .

Ans: Part a

The frequency of oscillation of LC circuit is .

Part b

The maximum charge on the capacitor is .

Part c

The maximum current through the inductor is .

Part d

The total energy possessed by the circuit at is .