Q 12-03-264JEE MainJEE Main 2019 (9 Apr, Shift 1)Easy
A wire of resistance $R$ is bent to form a square $ABCD$ as shown in the figure. The effective resistance between $E$ and $C$ is ($E$ is mid-point of arm $CD$)
Answer: (B) $\dfrac{7}{64}R$
Each side has resistance $R/4$. Between $E$ and $C$, the short path $EC$ is $R/8$; the long path $E\to D\to A\to B\to C$ is $R - R/8 = 7R/8$. They are in parallel:
$$R_{EC} = \frac{\frac R8\cdot\frac{7R}8}{R} = \frac{7R}{64}$$
Solution by Sreeraj P, M.Sc Physics