An alternating emf $\mathrm{E}=110 \sqrt{2} \sin 100 \mathrm{t}$ volt is applied to a capacitor of $2 \mu…

An alternating emf $\mathrm{E}=110 \sqrt{2} \sin 100 \mathrm{t}$ volt is applied to a capacitor of $2 \mu \mathrm{F}$, the rms value of current in the circuit is _____$\mathrm{mA}$,

Solution

$\begin{aligned} C & =2 \mu f ; \quad E=110 \sqrt{2} \sin (100 \mathrm{t}) \\ \mathrm{X}_{\mathrm{C}} & =\frac{1}{\omega \mathrm{c}}=\frac{1}{100 \times 2 \times 10^{-6}} \\ = & \frac{10000}{2}=5000 \Omega \\ \mathrm{i}_{\mathrm{o}} & =\frac{110 \sqrt{2}}{5000} \\ \mathrm{i}_{\mathrm{rms}} & =\frac{110 \sqrt{2}}{5000 \sqrt{2}} \\ & =\frac{110}{5} \mathrm{~mA} \\ & =22 \mathrm{~mA}\end{aligned}$

Asked in: JEE Main 2024 (08 Apr Shift 2)

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