Question

For the parallel resonant circuit given below, the value of the equivalent impedance of the circuit is ________

(a) 56.48 kΩ

(b) 78.58 kΩ

(c) 89.12 kΩ

(d) 26.35 kΩ

This question was posed to me in an online quiz.

Question is taken from Problems of Parallel Resonance Involving Quality Factor in chapter Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Right choice is (b) 78.58 kΩ

Easiest explanation: f = \(\frac{1}{2π\sqrt{LC}} \)

= \(\frac{1}{6.28\sqrt{(100×10^{-6})(162.11×10^{-12})}}\)

= \(\frac{1}{6.28\sqrt{1.621×10^{-14}}}\)

= \(\frac{1}{799×10^{-9}}\) = 1.25 MHz.

Inductive Reactance, XL = 2πfL = (6.28) (1.25×10^6)(100×10^-6)

= 785.394 Ω

Q = \(\frac{X_L}{R} = \frac{785.394}{7.85}\) = 100.05

∴ ZEQ = QXL = (100.05)(785.394) = 78.58 kΩ.