In connection with the extinction in circuit breaker, resistance switching is employed where in a resistance is placed in parallel with the poles of the circuit breaker as shown in the figure. This process introduces damping in the LC circuit. For critical damping the value of ‘r’ should be equal to

Option 3 : \(0.5\sqrt {\frac{L}{C}} \)

CT 1: Network Theory 1

11667

10 Questions
10 Marks
10 Mins

The characteristic equation for the given circuit is,

\({s^2} + \frac{1}{{RC}}s + \frac{1}{{LC}} = 0\)

By comparing with the standard second-order characteristic equation:

\({s^2} + 2\zeta {\omega _n}s + \omega _n^2 = 0\)

\({\omega _n} = \frac{1}{{\sqrt {LC} }}\)

\(2\zeta {\omega _n} = \frac{1}{{RC}} \Rightarrow \zeta = \frac{1}{{2R}}\sqrt {\frac{L}{C}} \)

For critical damping, ζ = 1

\( \Rightarrow r = 0.5\sqrt {\frac{L}{C}} \)