An inductor of 0.5,mH,a capacitor of 20,mu F | vedclass

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Question

(A) When the current is in phase with the $EMF$,the circuit is in resonance.At resonance,the inductive reactance equals the capacitive reactance,i.e.,

Vedclass · Accepted Answer

$242$

Vedclass · Answer

(A) When the current is in phase with the $EMF$,the circuit is in resonance.At resonance,the inductive reactance equals the capacitive reactance,i.e.,$X_L = X_C$.Therefore,the impedance of the circuit $Z$ is equal to the resistance $R$,so $Z = R = 20\,\Omega$.The $RMS$ current in the circuit is given by $I_{rms} = \frac{V_{rms}}{Z} = \frac{220\,V}{20\,\Omega} = 11\,A$.The amplitude (peak current) $I_0$ is related to the $RMS$ current by $I_0 = I_{rms} \sqrt{2}$.Substituting the value,$I_0 = 11 \sqrt{2} = \sqrt{121 	imes 2} = \sqrt{242}\,A$.Comparing this with $\sqrt{x}\,A$,we get $x = 242$.

An inductor of $0.5\,mH$,a capacitor of $20\,\mu F$ and a resistance of $20\,\Omega$ are connected in series with a $220\,V$ $AC$ source. If the current is in phase with the $EMF$,the amplitude of the current in the circuit is $\sqrt{x}\,A$. The value of $x$ is:

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