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An alternating voltage $V = 200 \sqrt{2} \sin (100 t)$ is connected to a $1$ microfarad capacitor through an ac ammeter. The reading of the ammeter shall be

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$10 m A$

$20 m A$

$40 m A$

$80 m A$

answer is B.

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Detailed Solution

$ω = 100 rad / s, C = 1 μF, V_{0} = 200 \sqrt{2} V$

$X_{C} = \frac{1}{ωC} = \frac{1}{100 \times (1 \times 10^{- 6})} = 10^{4} Ω$

Thus $I_{rms} = \frac{V_{rms}}{X_{C}} = \frac{(200 \sqrt{2} / \sqrt{2})}{10^{4}} = 20 \times 10^{- 3} A = 20 mA$ .

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