Question

(a) What is meant by "Resonance" in RLC circuits? Compare the series and parallel resonance circuits. (10)

(b) Find the frequency at which the following circuit resonates. (6)

Answer 1

Part (a)

Resonance is the condition in an RLC circuit when the inductive reactance equals the capacitive reactance (XL = XC). At resonance the circuit is purely resistive, the impedance is a minimum (series) or maximum (parallel), and the current is in phase with the voltage.
Series resonance: XL = XC, so the impedance Z = R (minimum). The current is a maximum and equals V/R. The voltage across the inductor and capacitor can be much larger than the supply voltage (voltage magnification). The resonant frequency f0 = 1/(2 pi sqrt(LC)). The power factor is unity.
Parallel resonance: XL = XC, so the admittance is a minimum and the impedance is a maximum. The line current is a minimum, while the circulating current in the L-C branch can be large (current magnification). The resonant frequency is approximately f0 = 1/(2 pi sqrt(LC)). The power factor is unity.
Comparison: in series resonance the impedance is minimum and current maximum; in parallel resonance the impedance is maximum and current minimum. Series resonance gives voltage magnification; parallel resonance gives current magnification. Series resonance is used in tuned circuits and filters; parallel resonance is used in rejector circuits and to improve power factor.

Part (b)

The resonant frequency of an RLC circuit is f0 = 1/(2 pi sqrt(L C)), where L is the inductance in henries and C the capacitance in farads.
(The numerical value depends on the values of L and C given in the figure; the method is to substitute the given L and C into f0 = 1/(2 pi sqrt(LC)).)

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