Question

In the diagram, resistance between any two junctions is R. Equivalent resistance across terminals A and B is

• A. $\frac{11R}{7}$
• B. $\frac{18R}{11}$
• C. $\frac{7R}{11}$
• D. $\frac{11R}{18}$

Answer 1

The correct option is D $\frac{11R}{18}$


$R_{CD}=\frac{R\times 2R}{R+2R}=\frac{2R}{3}$
Similarly, $R_{DB}==\frac{R\times 2R}{R+2}=\frac{2R}{3}R$
Now the equivalent circuit becomes

$R_{CB}=\frac{\frac{4R}{3}\times R}{\frac{4R}{3}+R}=\frac{4R^2}{3}\times \frac{3}{7R}=\frac{4R}{7}$

$R_{AB}=\frac{\frac{11R}{7}\times R}{\frac{11R}{7}+R}=\frac{11R^2}{7}\times \frac{7}{18R}=\frac{11R}{18}$