A LCR series circuit has the following parameters: L = 25 mH, C = 1.6 μF and R = 10 Ω. The circuit will be resonant at frequency
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → ~ 795 Hz
The resonant frequency of a series LCR circuit depends only on L and C; the resistance does not affect it.
\( \displaystyle f_0 = \frac{1}{2\pi\sqrt{LC}} \)
\( \displaystyle LC = 25\times10^{-3} \times 1.6\times10^{-6} = 4\times10^{-8}\,\mathrm{s^{2}} \)
\( \displaystyle \sqrt{LC} = 2\times10^{-4}\,\mathrm{s} \)
\( \displaystyle f_0 = \frac{1}{2\pi \times 2\times10^{-4}} \)
\( \displaystyle f_0 \approx 796\,\mathrm{Hz} \)