question_answer

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

A) R                                            

B) 2R

C) \[\frac{3R}{5}\]                                

D) 4R

Correct Answer: A

Solution :

The figure can be rearranged as, As,\[\frac{\text{resistance across AP}}{\text{resistance across AQ}}\]   \[=\frac{\text{resistance across PB}}{\text{resistance across QB}}\]\[\Rightarrow \]\[\frac{R}{R}=\frac{R}{R}=1\] It shows the balance conduction of Wheatstone bridge. So, the current through arm PQ is zero. The effective resistance between A and B. \[{{\operatorname{R}}_{eff}}\frac{2R\times 2R}{2R+2R}=\frac{2R}{2}=R\]