1.

A 50 μF capacitor, when connected in series with a coil having a resistance of 40Ω, resonates at 1000 Hz. The circuit is in resonating condition. The voltage across the capacitor is __________(a) 8.04 V(b) 7.96 V(c) 5.68 V(d) 1.25 VI had been asked this question during an internship interview.My question is based upon Advanced Problems on Resonance in section Resonance & Magnetically Coupled Circuit of Network Theory

Answer»

Correct choice is (c) 5.68 V

Easy explanation: At RESONANCE, | I | = \(\frac{V}{Z} = \frac{V}{R} \)

GIVEN that, R = 40Ω and V = 100 V

∴ | I | = \(\frac{100}{40}\) = 2.5 A

Power loss of the COIL = I^2 R = 2.5^2 × 40 = 250 W

Also, VC = IXC = 2.5 × \(\frac{1}{2πfC}\) and XC = \(\frac{1}{2πfC}\)

= 2.5 × \(\frac{1}{2π×1000×50×10^{-6}}\)

= 2.5 × \(\frac{100}{31.41}\) = 5.68 V.



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