Question

A radio tuner has an in-built L-C circuit to tune it for different radio stations broadcasting their programs. This circuit can tune to different frequencies by changing its resonance frequency. When broadcasting frequency and resonance frequency of L-C circuit are equal we are able to listen to the programs being broadcasted
(i) What is the resonance angular frequency of L-C circuit?
(ii) How is the resonance frequency of the LC circuit in the tuner changed?
(iii) How can the sharpness of resonance be increased?
(iv) If V is the initial voltage across the capacitor of LC circuit how much power

is consumed
(v) A transmitter operating at 1 MHz has LC circuit with L = 0.1mH, its

inductive reactance:​

Answer 1

Resonance circuits have variety of applications. They are as following:-

Tuning circuit of radio or TV set:-

Inside radio there is a circuit known as tuner circuit. This tuner circuit is LCR circuit.

Every radio has an antenna which receives signals from multiple stations.

When we are tuning the knob of the radio to connect to particular station we are changing the capacitance of the capacitor in the circuit.

As capacitance is changing the resistance also changes and when the natural frequency matches with the resonant frequency then the amplitude will attain the maximum value.

As a result we will be able to hear song.

When the amplitude is minimum we won’t be able to hear any song and when amplitude is near to maximum value we will be able to hear the song but the clarity won’t be very clear.

Problem:- A radio can tune over the frequency range of a portion of MW broadcast band: (800 kHz to 1200 kHz). If its LC circuit has an effective inductance of 200 μH, what must be the range of its variable capacitor?

Answer:-

The range of frequency (ν) of a radio is 800 kHz to 1200 kHz.

Lower tuning frequency, ν1 = 800 kHz = 800 × 103 Hz

Upper tuning frequency, ν2 = 1200 kHz = 1200 × 103 Hz

Effective inductance of circuit L = 200 μH = 200 × 10−6 H

Capacitance of variable capacitor for ν1 is given as:

C1 = (1/ω12L)

Where,

ω1 = Angular frequency for capacitor C1

= 2πν1

= 2π × 800 × 103 rad/s

∴ C1 = (1/ (2π × 800 × 103)2 × 200 × 10−6)

= 1.9809 × 10−10 F = 198 pF

Capacitance of variable capacitor for ν2 is given as:

C2 = (1/ω22L)

Where,

ω2 = Angular frequency for capacitor C2

= 2πν2

= 2π × 1200 × 103 rad/s

∴ C2 = (1/(2π × 1200 × 103)2 × 200 × 10−6

= 0.8804 × 10−10 F = 88 pF

Hence, the range of the variable capacitor is from 88.04 pF to 198.1 pF.