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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

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increased by 100%

reduced by 50%

increased by 75%

reduced by 75%

answer is D.

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Detailed Solution

$ω L = \frac{1}{ωC}$ (for resonance)
$ω^{2} = \frac{1}{LC}$ ..(i)
for case (ii)
${(2 ω)}^{2} = \frac{1}{{LC}_{1}}$ …(ii)
(ii) divided by (i)

$\Rightarrow 4 = \frac{C}{C_{1}} \Rightarrow C_{1} = \frac{C}{4}$
The capacitance is to be reduced by 75%.

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