Question

In the circuit shown below, if current is defined as the response signal of the circuit, then determine the transfer function.

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

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

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

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

I had been asked this question during an interview for a job.

My doubt stems from Transfer Function topic in portion Application of the Laplace Transform in Circuit Analysis of Network Theory

Answer 1

The correct answer is (c) H(s)=SC/(S^2 LC+RCS+1)

For explanation: If the current is defined as the response signal of the circuit, then the transfer function H (s) = I/V = 1/(R+sL+1/sC) = sC/(s^2Lc+RCs+1) where I corresponds to the output Y(s) and V corresponds to the input X(s).