Q 12-03-205JEE MainJEE Main 2021 (26 Feb, Shift 1)Medium
Five equal resistances are connected in a network as shown in figure. The net resistance between the points $A$ and $B$ is:
Answer: (A) $R$
Point $A$ is joined to $D$ and to $E$ through resistances $R$; point $B$ is joined directly to $C$. Resistances $R$ also join $D$–$E$, $D$–$C$ and $E$–$C$.
By symmetry, $D$ and $E$ are at the same potential, so no current flows in $DE$.
The two paths $A\to D\to C$ and $A\to E\to C$ each have resistance $2R$, and they are in parallel:
$$R_{AB} = \frac{2R\cdot 2R}{4R} = R$$
Solution by Sreeraj P, M.Sc Physics