Question

For the circuit given below, the driving point impedance is given by, Z(s) = \(\frac{0.2s}{s^2+0.1s+2} \). The component values are _________

(a) L = 5 H, R = 0.5 Ω, C = 0.1 F

(b) L = 0.1 H, R = 0.5 Ω, C = 5 F

(c) L = 5 H, R = 2 Ω, C = 0.1 F

(d) L = 0.1 H, R = 2 Ω, C = 5 F

I got this question in a job interview.

The origin of the question is Advanced Problems on Network Theorems in section Useful Theorems in Circuit Analysis of Network Theory

Answer 1

Correct choice is (d) L = 0.1 H, R = 2 Ω, C = 5 F

The explanation is: Dividing point impedance = R || sL || \(\frac{1}{sC} \)

= \(\Big\{\frac{(R)(\frac{1}{sC})}{R + \frac{1}{sC}}\Big\}\) || sL

= \(\frac{\frac{R}{1+sRC}}{\frac{R}{1+sRC}+sL} \)

= \(\frac{sRL}{s^2 RLC+sL+R} \)

Given that, Z(s) = \(\frac{0.2s}{s^2+0.1s+2} \)

∴ On comparing, we get L = 0.1 H, R = 2 Ω, C = 5 F.