Question

For the circuit shown in the figure below, the value of R for critical damping will be?

(a) 10.5 Ω

(b) 8.57 Ω

(c) 3.5 Ω

(d) 3 Ω

I got this question by my college professor while I was bunking the class.

My question is based upon Advanced Problems on Resonance in division Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

The correct answer is (b) 8.57 Ω

Easiest explanation: For a parallel RLC circuit, \(\frac{d^2 V}{dt^2} + \frac{1}{RC} \frac{dV}{dt} + \frac{V}{LC}\) = 0

Solving the 2nd order differential equation, we get, 2rωn = \(\frac{1}{RC}\) and ωn = \(\frac{1}{\sqrt{LC}}\)

As, r=1,

∴ R = \(\frac{1}{2} \sqrt{\frac{L}{C}} \)

= \(\frac{1}{2} \sqrt{\frac{7}{\frac{1}{42}}} = \frac{1}{2}\) × 17.15 = 8.57 Ω.