Question

Find the equivalent resistance between $A$ and $B$.

• A. $\frac{2r}{3}$
• B. $r$
• C. $\frac{r}{2}$
• D. $\frac{r}{3}$

Answer 1

The correct option is A $\frac{2r}{3}$

Given circuit is symmetrical about the line $123$ and it is perpendicular to $AB$.


So, due to the perpendicular axis symmetry, point $1$, $2$ and $3$ are equipotential. So resistors between them can be removed since current will not flow through them.

Now, the resistors between $A-1$ and $1-B$ are in series. Their equivalent resistance will be $r+r=2r$. Similarly resistors $A-2$, $2-B$ and $A-3$, $3-B$ have equivalent resistance $2r$.

Now all three are in parallel combination. Their equivalent resistance will be, $R_{AB}=\frac{2r}{3}$