A series LCR circuit with inductance 10 H , capacitance 10 μF , resistance 50 Ω is connected to an ac source of voltage, V = 200 (100 t) volt . If the - Physics MCQ NEET 2022 2026 | ExamTest.live

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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:

Solution & Step-by-step Explanation

From the voltage equation V = 200 sin (100 t), we have angular frequency of source ω = 100 rad/s .Frequency of source ν = \frac{ω}{2 π} = \frac{100}{2 π} = \frac{50}{π} Hz .Resonant angular frequency ω_{0} = \frac{1}{L C} : ω_{0} = \frac{1}{10 \times 10 \times 1 0 ^{- 6}} = \frac{1}{1 0 ^{- 4}} = \frac{1}{1 0 ^{- 2}} = 100 rad/s Resonant frequency ν_{0} = \frac{ω _{0}}{2 π} = \frac{100}{2 π} = \frac{50}{π} Hz .Thus, ν_{0} = ν = \frac{50}{π} Hz .

Try it yourself before checking the explanation above.

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:

ν_{0} = ν = 50 Hz

ν_{0} = ν = \frac{50}{π} Hz

ν_{0} = \frac{50}{π} Hz, ν = 50 Hz

ν_{0} = \frac{100}{π} Hz, ν = \frac{50}{π} Hz

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