$\frac{50}{\pi} \mu \mathrm{F}$ capacitor is connected to a $250 \mathrm{~V}, 50 \mathrm{~Hz}$ AC supply.…

$\frac{50}{\pi} \mu \mathrm{F}$ capacitor is connected to a $250 \mathrm{~V}, 50 \mathrm{~Hz}$ AC supply. Then the rms current of the circuit is
  1. $1.25 \mathrm{~A}$
  2. $4.9 \mathrm{~A}$
  3. $5 \mathrm{~A}$
  4. $6 \mathrm{~A}$

Solution

Given, $C=\frac{50}{\pi} \mu \mathrm{F}=\frac{50}{\pi} \times 10^{-6} \mathrm{~F}$ Source voltage, $ \begin{aligned} & V=250 \mathrm{~V} \\ & f=50 \mathrm{~Hz} \end{aligned} $ Capacitive reactance, $ \begin{aligned} & X_C=\frac{1}{2 \pi f C}=\frac{1}{2 \pi \times 50 \times \frac{50}{\pi} \times 10^{-6}}=200 \Omega \\ & I_{\mathrm{rms}}=\frac{V_{\mathrm{mms}}}{X_C}=\frac{250}{200}=1.25 \mathrm{~A} \end{aligned} $

Asked in: AP EAMCET 2022 (06 Jul Shift 2)

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