An inductor of inductance 2,mutext{H} is conn | vedclass

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Question

(B) For maximum current in an $LCR$ series circuit,the circuit must be in resonance.At resonance,the inductive reactance equals the capacitive reactan

Vedclass · Accepted Answer

$3872$

Vedclass · Answer

(B) For maximum current in an $LCR$ series circuit,the circuit must be in resonance.At resonance,the inductive reactance equals the capacitive reactance: $X_L = X_C$.$2\pi fL = \frac{1}{2\pi fC}$.Rearranging for capacitance $C$: $C = \frac{1}{4\pi^2 f^2 L}$.Given: $L = 2\,\mu	ext{H} = 2 	imes 10^{-6}	ext{ H}$,$f = 7\,	ext{kHz} = 7 	imes 10^3	ext{ Hz}$,and $\pi = \frac{22}{7}$.Substituting the values: $C = \frac{1}{4 	imes (\frac{22}{7})^2 	imes (7 	imes 10^3)^2 	imes 2 	imes 10^{-6}}$.$C = \frac{1}{4 	imes \frac{484}{49} 	imes 49 	imes 10^6 	imes 2 	imes 10^{-6}}$.$C = \frac{1}{4 	imes 484 	imes 2} = \frac{1}{3872}	ext{ F}$.Comparing this with $\frac{1}{x}	ext{ F}$,we get $x = 3872$.

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