Question

For the parallel resonant circuit given below, the current through the capacitor and inductor are _________

(a) IC = 10.892 mA; IL = 12.732 mA

(b) IC = 12.732 mA; IL = 10.892 mA

(c) IC = 10.892 mA; IL = 10.892 mA

(d) IC = 12.732 mA; IL = 12.732 mA

This question was posed to me during an interview.

I want to ask this question from Problems of Parallel Resonance Involving Quality Factor in section Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Right answer is (d) IC = 12.732 mA; IL = 12.732 mA

To explain: Resonant Frequency, 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

Capacitive Reactance, XC = \(\frac{1}{2πfC} = \frac{1}{(6.28)(1.25×10^6)(162.11×10^{-12})}\)

= \(\frac{1}{1.273×10^{-3}}\) = 785.417 Ω.

IC = \(\frac{V_A}{X_C} \)

= \(\frac{10}{785.417} \) = 12.732 mA

IL = \(\frac{V_A}{X_L} \)

= \(\frac{10}{785.394} \) = 12.732 mA.