Question

The resistance of all the wire between any two adjacent dots is $R$. The equivalent resistance between $A$ and $B$ as shown is

• A. $7R/13$
• B. $7R/6$
• C. $14R/8$
• D. $15R/7$

Answer 1

The correct option is B $7R/6$

Here the equivalent resistance of each triangle is

$R_{eq1}=\frac{(R+R)R}{(R+R)+R}=\frac{2R}{3}$

now, reduce the side by connecting resistance in series as shown in figure.

Here , $R_{eq2}=\frac{2R}{3}+\frac{2R}{3}=\frac{4R}{3}$

now the circuit is a balanced wheatstone bridge.So middle resistor $R$ is not working.

Thus, $R_{AB}=\frac{[\frac{4R}{2}+R][\frac{4R}{3}+R]}{[\frac{4R}{3}+R]+[\frac{4R}{3}+R]}$

$=\frac{\frac{49R^2}{9}}{\frac{14R}{3}}$

$=\frac{49R^2}{9}\times \frac{3}{14R}$

$=\frac{7}{6}R$