Question

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 V

I 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 1

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.