A series RLC circuit is assembled for a classroom demonstration

PHYSICS · Multi-part · CBSE · Physics · Alternating Current · Alternating Current

Problem

A series RLC circuit is assembled for a classroom demonstration. It consists of a resistor of

20\,\Omega

, an unknown air-cored inductor of negligible winding resistance, and a capacitor of

2.2\,\mu\text{F}

connected across an AC source of variable frequency whose peak voltage is

10\,\text{V}

. (i) Show that, at the frequency at which the circuit draws maximum current, the impedance of the circuit equals the resistance of the resistor. (ii) Starting from first principles, obtain an expression for the resonant frequency

f_0

of a series RLC circuit in terms of the inductance

L

and the capacitance

C

. (iii) The demonstration requires the current in the circuit to be maximum at

850\,\text{Hz}

(with an allowed deviation of

\pm 5\%

). Calculate the inductance that must be chosen. Express your answer in millihenry using scientific notation and state the permissible tolerance range for

L

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