Question

The equivalent resistance between points 1 and 4 of the circuit is :

• A. $\frac{8}{7}R$
• B. $\frac{7}{8}R$
• C. $\frac{15}{4}R$
• D. none of these

Answer 1

The correct option is A $\frac{8}{7}R$

As there is symmetry, disconnecting at 5,
Between 2 and 3,
$R$ is in parallel with $2R$,
So $R_{23}=\frac{2R}{3}$
As $R,\frac{2R}{3},R$ are in series
$R+\frac{2R}{3}+R=\frac{8R}{3}$
Between 1 and 4 ,
$2R$ is parallel to $\frac{8R}{3}$
$R_{14}=\frac{2R\times 8R/3}{2R+8R/3}=\frac{16R}{14}=\frac{8R}{7}$