Question

In the circuit shown below, if voltage across the capacitor is defined as the output signal of the circuit, then the transfer function is?

(a) H(s)=1/(S^2 LC-RCS+1)

(b) H(s)=1/(S^2 LC+RCS+1)

(c) H(s)=1/(S^2 LC+RCS-1)

(d) H(s)=1/(S^2 LC-RCS-1)

This question was addressed to me during a job interview.

Origin of the question is Transfer Function in division Application of the Laplace Transform in Circuit Analysis of Network Theory

Answer 1

Correct choice is (b) H(s)=1/(S^2 LC+RCS+1)

To elaborate: If the voltage across the capacitor is defined as the output signal of the circuit, the transfer function is H(s) = Vo/V = (1/sC)/(R+sL+1/sC)=1/(S^2LC+RCS+1).