An alternating voltage $E=200 \sqrt{2} \sin (100 t)$ volt is connected to a $1 \mu \mathrm{f}$ capacitor…

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

Solution

$\begin{aligned} & \mathrm{V}_{\mathrm{rms}}=\frac{\mathrm{I}_{\mathrm{rms}}}{\mathrm{X}_{\mathrm{C}}} \\ \therefore \quad \mathrm{I}_{\mathrm{ms}} & =\frac{\mathrm{V}_{\mathrm{o}} \omega \mathrm{C}}{\sqrt{2}}=\frac{200 \sqrt{2} \times 100 \times 1 \times 10^{-6}}{\sqrt{2}}=20 \mathrm{~mA}\end{aligned}$

Asked in: MHT CET 2023 (14 May Shift 2)

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