GATE 2015 EC – Question 40

Networks, Signals and Systems · Time and Frequency Domain Analysis of Linear Circuits · 2 marks · Multiple choice

The damping ratio of a series $RLC$ circuit can be expressed as

$\frac{R^2 C}{2L}$
$\frac{2L}{R^2 C}$
$\frac{R}{2}\sqrt{\frac{C}{L}}$
$\frac{2}{R}\sqrt{\frac{L}{C}}$

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Correct answer: (C) $\frac{R}{2}\sqrt{\frac{C}{L}}$

Explanation

For a series $RLC$ circuit, $\omega_n = \frac{1}{\sqrt{LC}}$ and $2\zeta\omega_n = \frac{R}{L}$. So $\zeta = \frac{R}{2L\omega_n} = \frac{R}{2}\sqrt{\frac{C}{L}}$.