Question

In a series resonant $$LCR$$ circuit, the voltage across $$R$$ is $$100\ volts$$ and $$R = 1k\ \Omega$$ with $$C=2\ \mu F$$. The resonant frequency is $$200\ rad/s$$. At resonance the voltage across $$L$$ is

A
4 x 103 V
B
2.5 x 102 V
C
40 V
D
250 V

Solution

The correct option is B $$250\ V$$The resonant angular frequency , $$\omega=\dfrac{1}{\sqrt{LC}}$$$$L=\dfrac{1}{\omega^2 C}=\dfrac{1}{200^2 \times 2\times 10^{-6}}=12.5 H$$At resonance , impedance $$Z=R$$ so the current in the circuit is $$I=\dfrac{V}{Z}=\dfrac{V}{R}=\dfrac{100}{1000}=0.1 A$$Voltage across inductor, $$V_L=IX_L=I\omega L=0.1\times 200\times 12.5=250 V$$Physics

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