Question

The equivalent resistance between the points aa of the electrical network shown in the figure is

• A. $6r$
• B. $4r$
• C. $3r$
• D. $r$

Answer 1

The correct option is D $r$

The equivalent circuit for the given electrical network is given in the first two diagrams.
This is a balanced wheatstone bridge, so the arm consisting $2r$ not in use. So, we have what is given in the last two diagrams.
So, the equivalent resistance between $a$ and $b$ is:
$\Rightarrow \frac{1}{r^{\prime }}=\frac{1}{2r}+\frac{1}{2r}\Rightarrow r^{\prime }=\frac{2r}{2}=r$