An ac source is connected in given series \(LCR\) circuit. The rms potential difference across the capacitor of \(20 \mu \mathrm{F}\) is _______\(v\). [\(\mathrm{V}=50 \sqrt{2} \sin 100 \mathrm{t}\) volt]

\(\mathrm{X}_{\mathrm{L}}=\omega \mathrm{L}=100 \times 1=100 \Omega\)
\(\mathrm{X}_{\mathrm{C}}=\frac{1}{\omega \mathrm{C}}=\frac{1}{100 \times 20 \times 10^{-6}}=500 \Omega\)
\(\mathrm{Z}=\sqrt{\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2+\mathrm{R}^2}\)
\(\sqrt{(100-500)^2+300^2}\)
\(\mathrm{Z}=500 \Omega\)
\(\mathrm{i}_{\text {ms }}=\frac{\mathrm{V}_{\text {ms }}}{\mathrm{Z}}=\frac{50}{500}=0.1 \mathrm{~A}\)
\(\text { rms voltage across capacitor }\)
\(\mathrm{V}_{\text {ms }}=\mathrm{X}_{\mathrm{C}} \mathrm{i}_{\mathrm{mms}}\)
\(=500 \times 0.1=50 \mathrm{~V}\)