Question

For the parallel resonant circuit given below, the value of the inductive and capacitive reactance is _________

(a) XL = 654.289 Ω; XC = 458.216 Ω

(b) XL = 985.457 Ω; XC = 875.245 Ω

(c) XL = 785.394 Ω; XC = 785.417 Ω

(d) XL = 125.354 Ω; XC = 657.215 Ω

The question was posed to me in examination.

The above asked question is from Problems of Parallel Resonance Involving Quality Factor topic in section Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Correct choice is (c) XL = 785.394 Ω; XC = 785.417 Ω

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.