Question

A capacitor, resistor of 10 Ω, and an inductor of 70 mH are in series with an ac source marked 120 V, 70 Hz. If it is found that voltage is in phase with the current, then find out the impedance of the circuit.

(a) 5 Ω

(b) 10 Ω

(c) 100 Ω

(d) 900 Ω

This question was addressed to me in an interview.

My doubt stems from AC Voltage Applied to a Series LCR Circuit in chapter Alternating Current of Physics – Class 12

Answer 1

Right option is (b) 10 Ω

The explanation is: XC = XL.

C = \(\frac {1}{4π^2f^2L}\)

C = \(\frac {1 \times 7 \times 7}{(4 \times 22 \times 22 \times 70^2 \times 70 \times 10^{-3} )}\)

C = 7.37 × 10^-5 F.

Impedance (Z) = √(R^2 + (XL – XC)^2

Z = 10 Ω.