The equivalent resistance of the network shown in figure between the points a and b will be

$r/3$

The correct answer is Option (2) → $r/3$

Label the resistors from left to right as R₁, R₂, R₃ each of resistance $r$.

– The top wire connects node a to the junction between R₂ and R₃.

– The bottom wire connects the junction between R₁ and R₂ directly to node b.

This gives node mapping:

• Node a and junction of R₂–R₃ are the same node.

• Node b and junction of R₁–R₂ are the same node.

Thus, R₁, R₂, R₃ are all in parallel.

Equivalent resistance: $ \frac{1}{R_{ab}} = \frac{1}{r} + \frac{1}{r} + \frac{1}{r} = \frac{3}{r} $

$R_{ab} = \frac{r}{3}$