Question

Each of the resistance in the network shown in figure is equal to R. The resistance between the terminals A and B is

• A. R
• B. 5R
• C. 3R
• D. 6r

Answer 1

The correct option is A R

The equivalent circuit is shown in fig. Since the Wheatstone's bridge is balanced, therefore no current will flow through the arm KL. Equivalent resistance between $AKM=R+R=2R$
Equivalent resistance between $ALM=R+R=2R$
The two resistances are in parallel. Hence equivalent resistance between A and B is given by
$\frac{1}{R^{\prime }}=\frac{1}{2R}+\frac{1}{2R}=\frac{2}{2R}=\frac{1}{R}\Rightarrow R^{\prime }=R$