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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

wL = $\frac{1}{{\omega c}}$ (for resonance)

${\omega ^2} = \frac{1}{{LC}}$

for case (ii)

${\left( {2\omega } \right)^2} = \frac{1}{{L{C_1}}}$

(ii) divide (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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