Find the peak current and resonant frequency of the following circuit (as shown in figure). (a) 2 A and 100 Hz (b) 2 A and 50 Hz (c) 0.2 A and 100 Hz (d) 0.2 A and 50 Hz

Answer: (d). Source: V₀ = 30 V, ω = 100 rad/s. XL = ω L = 100 × 0.1 = 10 Ω, XC = (1)/(ω C) = 1100×10⁻⁴ = 100 Ω Z = √(120² + 90²) = 150 Ω, so I₀ = 30/150 = 0.2 A. f₀ = (1)/(2π√(LC)) = 12π√0.1×10⁻⁴ = (316)/(2π) ≈ 50 Hz So the answer is (d) 0.2 A and 50 Hz.

Find the peak current and resonant frequency of the following circuit… | JEE Main 2021 (26 Feb, Shift 2)

Q97JEE Main 2021 · 26 FEB · SHIFT 2Medium

Resonance, Bandwidth & Q Factor

Find the peak current and resonant frequency of the following circuit (as shown in figure).

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Answer: (d)

Source: $V_0 = 30\text{ V}$ , $\omega = 100\text{ rad/s}$ .
$X_L = \omega L = 100 \times 0.1 = 10\ \Omega$ , $X_C = \frac{1}{\omega C} = \frac{1}{100\times10^{-4}} = 100\ \Omega$
$Z = \sqrt{120^2 + 90^2} = 150\ \Omega$ , so $I_0 = \frac{30}{150} = 0.2\text{ A}$ .
$f_0 = \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2\pi\sqrt{0.1\times10^{-4}}} = \frac{316}{2\pi} \approx 50\text{ Hz}$
So the answer is (d) 0.2 A and 50 Hz.

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