Question

Six identical resistors each of value $1\Omega$ are joined to form a regular hexagon. Further six more resistors of the same value are connected between the six vertices and the centre of the hexagon. The equivalent resistance between any two vertices lying opposite to each other is

• A. $\frac{5}{4}\Omega$
• B. $\frac{4}{5}\Omega$
• C. $\frac{3}{5}\Omega$
• D. $\frac{4}{3}\Omega$

Answer 1

The correct option is B $\frac{4}{5}\Omega$


Circuit is symmetrical about $AB$. Circuit can be redrawn as
Let each resistance be having a value $R$
$\Rightarrow R_{AB}=\left(\frac{8R}{3}\right)||\left(2R\right)||\left(\frac{8R}{3}\right)=\frac{4}{5}R\Omega =\frac{4}{5}\Omega$
Hence, the correct answer is (B).