# Question #11250

Dec 12, 2016

Let each of 12 resistors has got resistance $R$. The network of resistors connected in the circuit has been shown in the above figure.The equivalent network has also been shown here.

The equivalent resistance between A and C

${R}_{A C} = \frac{1}{\frac{1}{R} + \frac{1}{R} + \frac{1}{R}} = \frac{R}{3}$

The equivalent resistance between C and D

${R}_{C D} = \frac{1}{\frac{1}{R} + \frac{1}{R} + \frac{1}{R} + \frac{1}{R} + \frac{1}{R} + \frac{1}{R}} = \frac{R}{6}$

The equivalent resistance between D and B

${R}_{D B} = \frac{1}{\frac{1}{R} + \frac{1}{R} + \frac{1}{R}} = \frac{R}{3}$

The equivalent resistance between A and B

${R}_{A B} = {R}_{A C} + {R}_{C D} + {R}_{D B}$

$= \frac{R}{3} + \frac{R}{6} + \frac{R}{3} = \frac{5 R}{6}$