Question

A resistor of 50 Ω, an inductor of \(\frac {20}{\pi}\) H and a capacitor of \(\frac {5}{\pi }\) μF are connected in series to a voltage supply of 230 V – 50 Hz. Find the impedance of the circuit.

(a) 150 Ω

(b) 250 Ω

(c) 350 Ω

(d) 50 Ω

This question was addressed to me in an interview for internship.

Question is taken from AC Voltage Applied to a Series LCR Circuit in section Alternating Current of Physics – Class 12

Answer 1

The correct choice is (d) 50 Ω

The explanation is: XL = 2πfL

XL = 2π × 50 × \((\frac {20}{\pi })\) = 2000 Ω.

XC = \(\frac {1}{2πfC}\)

XC = 2000 Ω.

Z = √(R^2 + (XL – XC)^2

Z = √50^2 + (2000 – 2000)^2

Z = 50 Ω.