A series LCR circuit with inductance 10 H, capacitance 10 $μ$ F , resistance 50 $Ω$ is connected to an ac source of voltage, V=200 sin (100 t) volt. If the resonant frequency of the LCR circuit is $ν$ ₀ and the frequency of the ac source is $ν$ , then:

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$v_{0} = v = \frac{50}{π} Hz$

$v_{0} = \frac{50}{π} Hz, v = 50 Hz$

$v = 100 Hz; v_{0} = \frac{100}{π} Hz$

$v_{0} = v = 50 Hz$

answer is A.

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Detailed Solution

$\begin{array}{l} V = 200 \sin (100 t) \\ ν = \frac{50}{π} \\ ν_{0} = \frac{1}{2 π} \times \frac{1}{\sqrt{LC}} = \frac{1}{2 π} \frac{1}{\sqrt{10 \times 10^{- 5}}} = \frac{100}{2 π} = \frac{50}{π} \end{array}$

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