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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 kΩThis 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»

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.



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