A parallel plate capacitor made of circular plates each of radius $10 .0 cm$ has a capacitance $200 pF$ . The capacitor is connected to a $200 V AC$ supply with an angular frequency of $100 rad / s .$ . The RMS value of the conduction current is ______ $μA$ .

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answer is 4.

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Detailed Solution

Given : $E_{rms} = 200 V, ω = 100 rad / s$
Capacitance, $C = 200 \times 10^{- 12} F$
RMS value of the conduction current is:

$I_{rms} = \frac{E_{rms}}{X_{C}}$
$\Rightarrow I_{rms} = \frac{E_{rms}}{1 / ωC} = ωC \times E_{rms}$
$\Rightarrow I_{rms} = 100 \times 200 \times 10^{- 12} \times 200 = 4 \times 10^{- 6} A = 4 μA$

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