201902190310 Electric circuit diagrams (Elementary) Q6

The blogger claims no originality of his question below.

Circuit0002

In the figure above, the resistors are identical. Find the equivalent resistance between nodes:

Solution.

We label the nodes by $A$ , $B$ , $C$ , etc. Different nodes with the same electric potential will be labelled with the same label, as shown below:

Assuming resistors are identical, there is no current flowing through the central resistor between two equipotential end-nodes $B$ ‘s. Hence we draw the diagram below:

The equivalent resistance is $R_{\mathrm{eq}}=\displaystyle{\bigg( \frac{1}{R+R}+\frac{1}{R+R}\bigg)^{-1}}=R$ .(Alternatively one can use the $Y$ – $\Delta$ transformation.)
We draw the diagram below:

The equivalent resistance between nodes $c$ and $d$ is given by $\displaystyle{\frac{1}{R_{\mathrm{eq}}}}=\displaystyle{\frac{1}{R+R}}+\displaystyle{\frac{1}{R}}+\displaystyle{\frac{1}{R+R}}$ . Thus $R_{\mathrm{eq}}=\displaystyle{\frac{R}{2}}$ .
By $Y$ – $\Delta$ transformation.