A pocket radio employs a series LCR circuit as its tuning section

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A pocket radio employs a series LCR circuit as its tuning section. The inductance of the coil is

220\,\mu\text{H}

, and the capacitance is made variable by a gang capacitor. The effective resistance of the circuit at resonance is

4\,\Omega

. Answer the following: (i) Derive an expression for the resonant frequency

f_{0}

of a series LCR circuit in terms of the inductance

L

and the capacitance

C

only. (ii) Calculate the value of capacitance required to tune the receiver to a station transmitting at

800\,\text{kHz}

. (iii) For the value of

C

obtained in part (ii), determine the quality factor

Q

of the circuit, taking the resistance to be

4\,\Omega

. (iv) Using the result of part (iii), find the bandwidth (in kHz) of the circuit around

800\,\text{kHz}