Question

Given a series RLC circuit. The impedance Z(s) of the circuit will be?

(a) \(\frac{5(s^2+5)}{s^2+s+1}\)

(b) \(\frac{5(s^2-5)}{s^2-s-1}\)

(c) \(\frac{s^2-10s-100}{s}\)

(d) \(\frac{s^2+10s+100}{s}\)

The question was posed to me in an international level competition.

This key question is from Laplace Transform of a Periodic Function in section Application of the Laplace Transform in Circuit Analysis of Network Theory

Answer 1

The correct option is (d) \(\frac{s^2+10s+100}{s}\)

The best I can explain: The impedance Z(s) = R + sL + \(\frac{1}{sC}\)

 = \(\frac{s^2 LC+RCs+1}{sC}\)

This is similar to \(\frac{s^2+10s+100}{s}\).