Hello,

While practicing problems in preparation for my midterm next week, I came across the following question.

The network shown below (please see attachment) has poles at -1.5+((√111)/2) and -1.5-((√111)/2), and a zero at -3.

In addition, it is known that the impedance at zero frequency (s=0 or direct current) is 1 ohm, that is Z(0) = 1. Determine the values of R, L, C in the network.

I was easily able to determine the value of R by just getting Zeq and setting s = 0 to 1.
However, I don't know how to find the values of L and C. any help that can be rendered is much appreciated.

Thanks.

 

I don't have much experience with RLC networks, but the theory is this:

You construct the transfer function of the circuit and you convert it to its Laplace transformation. I suggest viewing the R,L and C components as "blocks" that are to be merged serially or parallely. This TF is a function of R, L and C.

You substitute R with the value you found. Afterwards, you calculate the poles and zeroes from the TF and you equate them with the ones given to get a system of 2 equations with 2 unknowns.