A resistor of 5 Ω, inductor of self inductance ((2)/(π²))H and a capacitor of unknown capacity are connected in series to an a.c. source of 100 V, 50 Hz supply. When the voltage and current are in phase, the value of capacitance is (a) 10 (b) 20 (c) 40 (d) 50

Answer: (d). In phase means resonance: C = (1)/(ω² L), ω = 100π. C = (1)/(10⁴π²·(2)/(π²)) = 12×10⁴ = 50×10⁻⁶ F So the answer is (d) 50 μ F.

A resistor of 5 Ω, inductor of self inductance ((2)/(π²))H and a… | MHT CET 2025 (26 Apr, Shift 1)

Q29MHT CET 2025 · 26 APR · SHIFT 1Medium

Resonance, Bandwidth & Q Factor

A resistor of $5\ \Omega$ , inductor of self inductance $\left(\frac{2}{\pi^2}\right)\text{H}$ and a capacitor of unknown capacity are connected in series to an a.c. source of $100\text{ V}, 50\text{ Hz}$ supply. When the voltage and current are in phase, the value of capacitance is

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Answer: (d)

In phase means resonance: $C = \frac{1}{\omega^2 L}$ , $\omega = 100\pi$ .
$C = \frac{1}{10^4\pi^2\cdot\frac{2}{\pi^2}} = \frac{1}{2\times10^{4}} = 50\times10^{-6}$ F
So the answer is (d) $50\ \mu$ F.

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Resonance, Bandwidth & Q Factor question from MHT CET 2025 (26 Apr, Shift 1)

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