Question

In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1µF and resistance R is 100 Ω . The frequency at which resonance occurs is :-

(1) 15.9 kHz
(2) 1.59 rad/s
(3) 1.59 kHz
(4) 15.9 rad/s

Answer 1

Correct option is (3) 1.59 kHz

L = 10 x 10^-3H

C = 1 x 10^-6F

R = 100 Ω

At resonance X_L = X_C

ωL = \(\frac{1}{ωC}\)

f = \(\frac{1}{2π\sqrt{LC}}\)

= \(\frac{1}{2π\sqrt{10\times10^{-3}\times\ 10^{-6}}}\)

= 1.59 KHz