1. ν = 100 Hz ; ν₀ = 100/π Hz 2. ν₀ = ν = 50 Hz 3. ν₀ = ν = 50/π Hz 4. ν₀ = 50/π Hz, ν = 50 Hz

Answer: 3. ν₀ = ν = 50/π Hz Compare the source frequency with the resonant frequency. Source: ω=100\ rad/s⇒ν=100/2π=50/π Hz. Resonance: ω₀=1/√(LC)=dfrac1sqrt10×10×10⁻⁶=100\ rad/s⇒ν₀=50/π Hz. So ν₀=ν=50/π Hz, option (3).

Topic: Reactance, impedance, LCR series circuit, resonance· Electromagnetic Induction and Alternating Currents

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 resonant frequency of the LCR circuit is _0 and the frequency of the ac source is , then :

1. \(\nu = 100\) Hz ; \(\nu_0 = \frac{100}{\pi}\) Hz

2. \(\nu_0 = \nu = 50\) Hz

3. \(\nu_0 = \nu = \frac{50}{\pi}\) Hz

4. \(\nu_0 = \frac{50}{\pi}\) Hz, \(\nu = 50\) Hz

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Answer: 3. \(\nu_0 = \nu = \frac{50}{\pi}\) Hz

Compare the source frequency with the resonant frequency.

Source: \(\omega=100\ \text{rad/s}\Rightarrow\nu=\dfrac{100}{2\pi}=\dfrac{50}{\pi}\) Hz.

Resonance: \(\omega_0=\dfrac{1}{\sqrt{LC}}=\dfrac{1}{\sqrt{10\times10\times10^{-6}}}=100\ \text{rad/s}\Rightarrow\nu_0=\dfrac{50}{\pi}\) Hz.

So \(\nu_0=\nu=50/\pi\) Hz, option (3).

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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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 resonant frequency of the LCR circuit is _0 and the frequency of the ac source is , then :

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