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Q.

A given LCR series circuit satisfies the condition for resonance with a given AC source. If the angular frequency of the AC source is increased by 100% then in order to establish resonance, without changing the value of inductance, the capacitance must be

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a

increased by 100%

b

Reduced by 50%

c

increased by 75%

d

reduced by 75%

answer is D.

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Detailed Solution

ωL=1ωc(for resonance)ω2=1LC. . . (i)for case (ii) (2ω)2=1LC1 . . (ii)(ii) divide (i) ⇒4 = =CC1⇒C1=C4The capacitance is to be reduced by 75%.
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A given LCR series circuit satisfies the condition for resonance with a given AC source. If the angular frequency of the AC source is increased by 100% then in order to establish resonance, without changing the value of inductance, the capacitance must be