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STD 12 -7. Alternating current — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 12 -7. Alternating current4 Marks
Question
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

✓

Answer

$\mathrm{X}_{\mathrm{L}}=\omega \mathrm{L}=100 \times 1=100 \Omega$

$\mathrm{X}_{\mathrm{C}}=\frac{1}{\omega \mathrm{C}}=\frac{1}{100 \times 20 \times 10^{-6}}=500 \Omega$

$\mathrm{Z}=\sqrt{\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2+\mathrm{R}^2}$

$\sqrt{(100-500)^2+300^2}$

$\mathrm{Z}=500 \Omega$

$\mathrm{i}_{\text {ms }}=\frac{\mathrm{V}_{\text {ms }}}{\mathrm{Z}}=\frac{50}{500}=0.1 \mathrm{~A}$

$\text { rms voltage across capacitor }$

$\mathrm{V}_{\text {ms }}=\mathrm{X}_{\mathrm{C}} \mathrm{i}_{\mathrm{mms}}$

$=500 \times 0.1=50 \mathrm{~V}$

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