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(C) In an $LCR$ series circuit, the current is in phase with the emf when the circuit is in resonance.At resonance, the inductive reactance $X_L$ equa

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$242$

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(C) In an $LCR$ series circuit, the current is in phase with the emf when the circuit is in resonance.At resonance, the inductive reactance $X_L$ equals the capacitive reactance $X_C$, and the impedance $Z$ of the circuit is equal to the resistance $R$.Given: $R = 20 	ext{ } \Omega$, $V_{rms} = 220 	ext{ V}$.The peak voltage (amplitude of emf) is $V_0 = V_{rms} \sqrt{2} = 220 \sqrt{2} 	ext{ V}$.At resonance, the impedance $Z = R = 20 	ext{ } \Omega$.The amplitude of the current $I_0$ is given by $I_0 = \frac{V_0}{Z} = \frac{220 \sqrt{2}}{20} = 11 \sqrt{2} 	ext{ A}$.We can write $I_0 = \sqrt{11^2 	imes 2} = \sqrt{121 	imes 2} = \sqrt{242} 	ext{ A}$.Comparing this with the given form $[x]^{1/2} 	ext{ A}$, we get $x = 242$.

An inductor of $0.5 \text{ mH}$, a capacitor of $20 \text{ } \mu\text{F}$ and resistance $20 \text{ } \Omega$ are connected in series with a $220 \text{ V}$ ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $[x]^{1/2} \text{ A}$. The value of $x$ is

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