For the network shown in figure,

If 1 A current enter the circuit through a, then:

$\begin{array}{l}-x-(x-y)+3(1-x)=0\\ 5x-y=3 .......\left(1\right)\\ -y+5(1-y)+(x-y)=0\\ x-yy=-5 .......\left(2\right)\end{array}$
$$\begin{gathered} \text{ Solving, }\mathrm{x}=\frac{13}{17}\mathrm{A};\mathrm{y}=\frac{14}{17}\mathrm{A} \\ \begin{array}{l}{\mathrm{V}}_{\mathrm{A}}-\frac{13}{17}-\frac{14}{17}={\mathrm{V}}_{\mathrm{B}}{\mathrm{V}}_{\mathrm{A}}-{\mathrm{V}}_{\mathrm{B}}=\frac{27}{17}\mathrm{V}\\ \therefore {\mathrm{R}}_{\mathrm{AB}}=\frac{{\mathrm{V}}_{\mathrm{A}}-{\mathrm{V}}_{\mathrm{B}}}{1}=\frac{27}{11}\mathrm{\Omega }\end{array} \end{gathered}$$