question_answer

In a given Wheatstone's network\[\operatorname{P}=2\,\Omega ,\,\,Q=\,\,2\,\,\Omega ,\,\,R=2\,\,\Omega \,\,and\,\,5=3\,\Omega \], calculate the value of resistance with which S is to be shunted so that bridge get balanced.

A) 2                                

B) 3

C) 6                                

D) 9

Correct Answer: C

Solution :

Let resistance r Q, be shunted with resistance S, so that bridge gets balanced. If S is the equivalent resistance of S and r, In balanced position \[\frac{P}{Q}=\frac{R}{S'}\] \[\therefore \,\,\,\,\,\,\,\,\,\,\frac{2}{z},\,\,\frac{2}{5}\,\,\Rightarrow \,\,\,S'=2\,\Omega \] Now,      \[\frac{1}{S'}=\frac{1}{S}+\frac{1}{r}\] \[\Rightarrow \,\,\,\,\,\,\frac{1}{r}=\frac{1}{S}-\frac{1}{S}=\frac{1}{2}-\frac{1}{3}=\frac{3-2}{6}\] \[\frac{1}{r}=\frac{1}{6}\,\,\,\Rightarrow \,\,r=6\,\Omega \,\]