1.

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 ΩI 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»

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.



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