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

Question

In an LC circuit, the inductance $ L $ is 2 H and the capacitance $ C $ is 4 Î¼F. What is the frequency of oscillation of the circuit?

Answer 1

Step 1: Plan:
Find the rms current first, then the amplitude.

Step 2: Steps:
At resonance the rms current is $\frac{220}{20} = 11$ A. The amplitude is $\sqrt2$ times that, so $I_0 = 11\sqrt2 = \sqrt{121\times2} = \sqrt{242}$ A.
So $x = 242$. The values of $L$ and $C$ only fix the resonance frequency and do not enter the answer.

Final Answer:
The value of $x$ is $242$, option (C). \[ \boxed{242} \]

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

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The Correct Option is C

Solution and Explanation

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