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(i) A series LCR circuit is connected to an a.c. source of variable frequency. Draw a suitable phasor diagram to deduce the expressions for the amplitude of the current and phase angle. 

(ii) Obtain the condition at resonance. Draw a plot showing the variation of current with the frequency of a.c. source for two resistances R1 and R2 (R1 > R2). Hence define the quality factor, Q and write its role in the tuning of the circuit.

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Best answer

(i)

From the phasor diagram

Magnitude of net voltage

A larger value of quality factor corresponds to a sharper resonance.

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