Current Electricity question for JEE Main (JEE Main 2025 (28 Jan, Shift 1)), with solution

Answer: (A) $\dfrac{r}{9}$

Label the junctions along the line: left end $L$, then $P$ (between the first and second resistors), then $Q$ (between the second and third), then the right end $R'$.

- The upper wire joins $L$ to $Q$, so $L$ and $Q$ are the same node.
- The lower wire joins $P$ to $R'$, so $P$ and $R'$ are the same node.

Each $r/3$ resistor now connects the node $\{L, Q\}$ to the node $\{P, R'\}$: all three are in parallel between the two ends.
$$R_{eq} = \frac{r/3}{3} = \frac{r}{9}$$

Solution by Sreeraj P, M.Sc Physics