Question

In the figure shown, segments $AB,BC,CD$ and $DA$ , as well as the diagonal segments $AC$ and $BD$ have a resistance $2\,\Omega$ each. The mid points of the diagonal wires are soldered with each other. If the effective resistance between the mid points of sides $AD$ and $CD$ is $\frac{x}{4}\,\Omega$ , find the value of $x$ .

Answer 1

The given circuit is as shown:

Since the circuit is symmetric about $AB$ , it can be simplified as

Therefore, the effective resistance
$R_{AB}=\left(1 + \frac{4 \times 2}{4 + 2} + 1\right)\left|\right.\left|\right.\left(1 + 1\right)$
$\Rightarrow R_{AB}=\frac{\frac{20}{6} \times 2}{\frac{20}{6} + 2}=\frac{40}{32}$
$\Rightarrow R_{AB}=1.25\,\Omega$