1.

For the series resonant circuit given below, the value of the inductive and capacitive reactance is _________(a) XL = 5.826 kΩ; XC = 5.826 kΩ(b) XL = 2.168 kΩ; XC = 2.168 kΩ(c) XL = 6.282 kΩ; XC = 6.282 kΩ(d) XL = 10.682 kΩ; XC = 10.682 kΩI have been asked this question in my homework.I'm obligated to ask this question of Problems of Parallel Resonance Involving Quality Factor topic in portion Resonance & Magnetically Coupled Circuit of Network Theory

Answer»

The CORRECT OPTION is (c) XL = 6.282 kΩ; XC = 6.282 kΩ

The BEST I can explain: Resonant Frequency, \(\FRAC{1}{2π\sqrt{LC}} \)

= \(\frac{1}{6.28\sqrt{(4.7×10^{-3})(0.001×10^{-6})}}\)

= \(\frac{1}{6.28\sqrt{4.7×10^{-12}}}\)

= \(\frac{1}{1.362×10^{-5}}\) = 73.412 kHz

Inductive Reactance, XL = 2πfL = (6.28) (73.142 × 10^3)(4.7 × 10^-6)

= 2.168 kΩ

Capacitive Reactance, XC = \(\frac{1}{2πfC} = \frac{1}{(6.28)(73.142×10^3)(0.001×10^{-6})}\)

= \(\frac{1}{4.613×10^{-4}}\) = 2.168 kΩ.



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