Resistance Network (Part 5)

We note that resistance network is symmetrical about the line $CC'$ . Then $|V_{AC}| = |V_{BC}| = |V_{AC'}| = |V_{BC'}| = \frac 12 |V_{AB}|$ . This means that point $C$ and point $C'$ are equipotential and can be considered as a single point $C$ . The equivalent circuit for the resistance network is as the right figure. The equivalent resistance is given by:

$\begin{aligned} R_{AB} & = 2 \big(2\ ||\ (1+ 1\ ||\ 1) \big) \\ & = 2 \left(2\ ||\left(1+ \frac 12\right) \right) \\ & = 2 \left(2\ ||\ \frac 32 \right) \\ & = \frac {12}7 \approx \boxed{1.714} \ \Omega \end{aligned}$

We can also separate the wires at the point of intersection of the squares