NEET 2022 · PhysicsResonant frequencyPrevious Year Question
A series LCR circuit with inductance 10 H, capacitance 10 μF, 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 v₀ and the frequency of the ac source is v, then:
Answer: (B) v = v₀ = 50/π Hz. Answer: (B) v = v₀ = 50/π Hz Solution: From V = 200 sin(100 t): ω = 100 rad/s ⇒ source frequency v = ω/2π = 100/2π = 50/π Hz.
- A.v = v₀ = 50 Hz
- B.v = v₀ = 50/π Hz✓
- C.v = 50/π Hz, v₀ = 50 Hz
- D.v₀ = 100/π Hz; v = 100 Hz
Correct Answer
(B) v = v₀ = 50/π Hz
Solution & Explanation
Answer: (B) v = v₀ = 50/π Hz Solution: From V = 200 sin(100 t): ω = 100 rad/s ⇒ source frequency v = ω/2π = 100/2π = 50/π Hz. Resonant frequency v₀ = 1/(2π√(LC)) = 1/(2π√(10 × 10×10⁻⁶)) = 1/(2π×10⁻²) = 50/π Hz. Hence v = v₀ = 50/π Hz (circuit at resonance).
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