Question

Given, R = 10 Ω, L = 100 mH and C = 10 μF. The values of ω0, ω1 and ω2 respectively are?

(a) ω0 = 1000 rad/s, ω1 = 951.25 rad/s, ω2 = 1075.54 rad/s

(b) ω0 = 1000 rad/s, ω1 = 975.25 rad/s, ω2 = 1051.25 rad/s

(c) ω0 = 1000 rad/s, ω1 = 951.25 rad/s, ω2 = 1051.25 rad/s

(d) ω0 = 1000 rad/s, ω1 = 825.30 rad/s, ω2 = 1075.54 rad/s

I have been asked this question in an interview for internship.

Question is from Problems of Series Resonance Involving Frequency Response of Series Resonant Circuit in portion Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Correct option is (c) ω0 = 1000 rad/s, ω1 = 951.25 rad/s, ω2 = 1051.25 rad/s

To explain I would say: ω0 = \(\frac{1}{\sqrt{100×10^{-3}×10×10^{-6}}}\) = 1000 rad/s

Now, ω1 = \(\frac{-R + \sqrt{R^2 + \frac{4L}{C}}}{2L} = \frac{-10 + \frac{\sqrt{100 + 4 × 100 × 10^{-3}}}{10×10^{-6}}}{2×100×10^{-3}}\) = 951.25 rad/s

And, ω2 = \(\frac{+R+ \sqrt{R^2+ 4L/C}}{2L}\) = 1051.25 rad/s.