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  • A series LCR circuit with inductance ,capacitance , and

A series LCR circuit with inductance \mathrm{10H},capacitance \mathrm{10\mu F}, and resistance \mathrm{50\Omega} is connected to an ac source of voltage,

\mathrm{V=200\sin (100t)} volts, If the resonant frequency of the LCR circuit is \nu_0 and the frequency of the ac source is \nu, then :

Option: 1

\mathrm{\nu_{0}=\nu=\frac{50}{\pi} \mathrm{Hz}} \\


Option: 2

\mathrm{\nu_{0}=\frac{50}{\pi} \mathrm{Hz}, \nu=50 \mathrm{~Hz}} \\


Option: 3

\mathrm{\nu=100 \mathrm{~Hz} ; \nu_{0}=\frac{100}{\pi} \mathrm{Hz} }\\


Option: 4

\mathrm{\nu_{0}=\nu=50 \mathrm{~Hz}}


Answers (1)

best_answer

 \begin{aligned} & \mathrm{V}=200 \sin (100 \mathrm{t}) \\ & \nu=\frac{50}{\pi} \\ & \nu_0=\frac{1}{2 \pi} \times \frac{1}{\sqrt{\mathrm{LC}}}=\frac{1}{2 \pi} \frac{1}{\sqrt{10 \times 10^{-5}}}=\frac{100}{2 \pi}=\frac{50}{\pi} \end{aligned}

Hence the correct option is 1

Posted by

manish

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