An alternating voltage $v=200 \sqrt{2} \sin (100 t)$ is connected to a $1 \mu \mathrm{~F}$ capacitor through…

An alternating voltage $v=200 \sqrt{2} \sin (100 t)$ is connected to a $1 \mu \mathrm{~F}$ capacitor through an a. c. ammeter. The reading of the ammeter shall be
  1. 10 mA
  2. 20 mA
  3. 40 mA
  4. 80 mA

Solution

Alternating voltage: $\mathrm{e}=200 \sqrt{2} \sin (100 \mathrm{t})$ volt Comparing with $\mathrm{e}=\mathrm{e}_0 \sin \omega t$ $\omega=100 \mathrm{rad} / \mathrm{s}, \mathrm{e}_0=200 \sqrt{2}$
Capacitive reactance, $\begin{aligned} & \mathrm{X}_{\mathrm{C}}=\frac{1}{\omega \mathrm{C}}=\frac{1}{100 \times 10^{-6}} \Omega=10^4 \Omega \\ & \mathrm{I}_0=\frac{\mathrm{e}_0}{\mathrm{X}_{\mathrm{C}}} \\ & \mathrm{I}_0=\frac{200 \sqrt{2}}{10^4} \\ & \mathrm{I}_0=2 \sqrt{2} \times 10^{-2} \mathrm{~A} \\ & \mathrm{I}_{\mathrm{rmi}}=\frac{\mathrm{I}_0}{\sqrt{2}}=\frac{2 \sqrt{2} \times 10^{-2}}{\sqrt{2}}=2 \times 10^{-2} \cdot \mathrm{~A}=20 \mathrm{~mA} \end{aligned}$

Asked in: MHT CET 2024 (03 May Shift 1)

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