Right option is (d) (8 S+2)/(8 S+4)
Explanation: From the circuit, the parallel combination of resistance and capacitance can be combined into equivalent in impedance. Zeq(S) = 1/(2 S+1/2)=2/(4 S+1). Applying Kirchhoff’s laws, we have V2 (S) = 2 I1(S) => V1 (S) = I1 (S)[2/(4 S+1)+2]
= I1 (S)[(8 S+4)/(4 S+1)] The transfer function G21 (s) = V2(s)/V1(s) = 2 I1(S)/((8 S+4)/(4 S+1))I1(S) = (8 S+2)/(8 S+4).