In a series LCR circuit, $\text{R = 1k}\Omega,\text{C}=2\mu\text{F}$ and voltage across R is 100V. The resonant frequency of the circuit $\omega$ is 200 rad $s^{-1}$. Calculate the value of voltage across L at resonance.
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Current flowing in the circuit is
$\text{I}=\frac{\text{V}_{\text{R}}}{\text{R}}=\frac{100}{1000}=0.1\text{A}$
$\therefore$ Also at resonance, $\omega\text{L}=\frac{1}{\omega\text{C}}$
$\omega\text{L}=\frac{1}{200\times2\times10^{-6}}=2500\Omega$
$\therefore$ Volage across, $\text{L = I}(\omega\text{L})=0.1\times2500=250\text{V}$
$\text{I}=\frac{\text{V}_{\text{R}}}{\text{R}}=\frac{100}{1000}=0.1\text{A}$
$\therefore$ Also at resonance, $\omega\text{L}=\frac{1}{\omega\text{C}}$
$\omega\text{L}=\frac{1}{200\times2\times10^{-6}}=2500\Omega$
$\therefore$ Volage across, $\text{L = I}(\omega\text{L})=0.1\times2500=250\text{V}$
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