Question

For the series circuit given below, the value of the voltage across the capacitor and inductor are _____________

(a) VC = 16.306 V; VL = 16.306 V

(b) VC = 11.268 V; VL = 11.268 V

(c) VC = 16.306 V; VL = 16.306 V

(d) VC = 14.441 V; VL = 14.441 V

I have been asked this question at a job interview.

This intriguing question comes from Problems of Parallel Resonance Involving Quality Factor in portion Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Right option is (c) VC = 16.306 V; VL = 16.306 V

Best explanation: Resonant Frequency, \(\frac{1}{2π\sqrt{LC}} \)

= \(\frac{1}{6.28\sqrt{(4.7×10^{-3})(0.001×10^{-6})}}\)

= \(\frac{1}{6.28\sqrt{4.7×10^{-12}}}\)

= \(\frac{1}{1.362×10^{-5}}\) = 73.412 kHz

Inductive Reactance, XL = 2πfL = (6.28) (73.142 × 10^3)(4.7 × 10^-6)

= 2.168 kΩ

Capacitive Reactance, XC = \(\frac{1}{2πfC} = \frac{1}{(6.28)(73.142×10^3)(0.001×10^{-6})}\)

= \(\frac{1}{4.613×10^{-4}}\) = 2.168 kΩ

ZEQ = R = 47 Ω

IT = \(\frac{V_{in}}{Z_{EQ}}  = \frac{V_{in}}{R} = \frac{0.3535}{47}\) = 7.521 mA

∴ Voltage across the capacitor, VC = XCIT = (2.168 kΩ)(7.521 mA) = 16.306 V

∴ Voltage across the inductor, VL = XLIT = (2.168 kΩ)(7.521 mA) = 16.306 V.