Question

Nine wires each of resistance $r=2\Omega$ are connected to make a prism as shown in Figure. Find the equivalent resistance of the arrangement across $AB$ (in $\Omega$).

Answer 1

Potential drop after $R_1$ and $R_2$, is same.

i.e. $V_P=V_Q⟹$ There will be no current through $R_3⟹$ we can neglect $R_3$.

Similarly, potential drop after $R_5$ and $R_4$ is same, i.e $U_R=U_S⟹$ there will be no current through arm $R_9⟹$ we can neglect $R_9$

$\therefore$ after neglecting $R_3$ and $R_9$, $(R_2,R_5,R_7),(R_1,R_4,R_9)$ these set are in series and they are in parallel with $R_6$.

$⟹\frac{1}{R_{eq}}=\frac{1}{3R}+\frac{1}{3R}+\frac{1}{R}=\frac{5}{3R}$

$⟹R_{eq}=\frac{3R}{5}\Omega$ given $R=2⟹,R_{eq}=\frac{6}{5}\Omega$