In an ac circuit, an alternating voltage e=200 √{2} sin 100 t volts is connected to a capacitor of

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7.Alternating Current

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In an $ac$ circuit, an alternating voltage $e=200 \sqrt{2} \sin 100 t$ volts is connected to a capacitor of capacitance $1 \;\mu F$. The rms value of the current in the circuit is ..... $mA$

A

$10$

B

$20$

C

$100$

D

$200$

(AIPMT-2011)

Solution

$e=200 \sqrt{2} \sin 100 t$

$\omega=100 \frac{ rad }{ sec }$

$E_{\text {rms }}=\frac{200 \sqrt{2}}{\sqrt{2}}$

$C=1 \times 10^{-6}$

$Z=X_c=\frac{1}{\omega C}=\frac{1}{100 \times 10^{-6}}=10^4\; \Omega$

$I=\frac{E_{r m s}}{Z}=\frac{\frac{200 \sqrt{2}}{\sqrt{2}}}{10^4}=2 \times 10^{-2} A=20 \;mA$

Standard 12

Physics

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