An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of $20 \mu \mathrm{F}$ is _____V.

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Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{X}_{\mathrm{L}}=\omega \mathrm{L}=100 	imes 1=100 \Omega \ & \mathrm{X}_{\mathrm{C}}=\frac{1}{\omega \mathrm{C}}=\frac{1}{100 	imes 20 	imes 10^{-6}}=500 \Omega \ & \mathrm{Z}=\sqrt{\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}ight)^2+\mathrm{R}^2} \ & \sqrt{(100-500)^2+300^2} \ & \mathrm{Z}=500 \Omega \ & \mathrm{i}_{	ext {rms }}=\frac{\mathrm{V}_{	ext {rms }}}{\mathrm{Z}}=\frac{50}{500}=0.1 \mathrm{~A} \ & 	ext { rms voltage across capacitor } \ & \mathrm{V}_{	ext {rms }}=\mathrm{X}_{\mathrm{C}} \mathrm{i}_{	ext {rms }} \ & =500 	imes 0.1=50 \mathrm{~V}\end{aligned}$

An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of…

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