The network function \(f(s)= \dfrac{(s+2)}{(s+1)(s+3)}\), represe
A. RC impedance
B. RL impedance
C. RC impedance and RL admittance
D. RC admittance and RL impedance
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
Concept
Laplace transform RL and RC circuit is given below:
Laplace transform
In the case of Impedance
\(L \to Ls\) , \( C \to \frac{1}{{Cs}}\)
In the case of Admittance
\(L \to \frac{1}{{Ls}}, C \to Cs\)
Given:
\( f\left( s \right) = \frac{{s + 2}}{{\left( {s + 1} \right)\left( {s + 3} \right)}}\)
By partial fraction
\(\frac{{s + 2}}{{\left( {s + 1} \right)\left( {s + 3} \right)}} = \frac{A}{{s + 1}} + \frac{B}{{s + 3}}\)
\( A\left( {s = - 1} \right) = \frac{1}{2},B\left( {s = - 3} \right) = \frac{1}{2}\)
\(f\left( s \right) = \frac{1}{{2\left( {s + 1} \right)}} + \frac{1}{{2\left( {s + 3} \right)}}\)
\({z_1} = \frac{1}{{2s + 2}},\;{z_2} = \frac{1}{{2s + 6}}\)
So, the given network function is of RL impedance.
