The resonant frequency of a series LCR circuit with L = 3H, C = 27 μF and R = 20Ω will be:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 111 rad/s
A series LCR circuit is at resonance when the inductive and capacitive reactances are equal, \( \omega_0L = 1/(\omega_0C) \). This gives the angular resonant frequency \( \omega_0 = 1/\sqrt{LC} \), which does not depend on R.
\( LC = 3\,\mathrm{H}\times27\times10^{-6}\,\mathrm{F} = 81\times10^{-6}\,\mathrm{s^{2}} \)
\( \displaystyle \omega_0 = \frac{1}{\sqrt{81\times10^{-6}}} = \frac{1}{9\times10^{-3}}\,\mathrm{rad/s} \approx 111\,\mathrm{rad/s} \)