In an $\mathrm{AC}$ circuit an alternating voltage $e=200 \sqrt{2} \sin 100 t$ volt is connected to a…

In an $\mathrm{AC}$ circuit an alternating voltage $e=200 \sqrt{2} \sin 100 t$ volt is connected to a capacitor of capacity $1 \mu \mathrm{F}$. The rms value of the current in the circuit is
  1. $100 \mathrm{~mA}$
  2. $200 \mathrm{~mA}$
  3. $20 \mathrm{~mA}$
  4. $10 \mathrm{~mA}$

Solution

Given, $e=200 \sqrt{2} \sin 100 t$ and $\begin{aligned} C & =1 \mu \mathrm{F} \\ E_{\mathrm{rms}} & =200 \mathrm{~V} \\ X_C & =\frac{1}{\omega C}=\frac{1}{1 \times 10^{-6} \times 100}=10^4 \Omega \\ i_{\mathrm{rms}} & =\frac{E_{\mathrm{rms}}}{X_C} \\ i_{\mathrm{rms}} & =\frac{200}{10^4}=2 \times 10^{-2} \mathrm{~A}=20 \mathrm{~mA} \end{aligned}$

Asked in: MHT CET Full Test 13

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