question_answer

Three resistances \[P,\,\,\,Q,\,\,\,R\] each of \[2\,\,\Omega \] and an unknown resistance \[S\] form the four arms of a Wheatstone's bridge circuit. When a resistance of \[6\,\,\Omega \] is connected in parallel to \[S\] the bridge gets balanced. What is the value of\[S?\]

A) \[2\,\,\Omega \]                                             

B) \[3\,\,\Omega \]

C)  \[6\,\,\Omega \]                                            

D)  \[1\,\,\Omega \]

Correct Answer: B

Solution :

Key Idea The bridge formed with given resistances is a balanced Wheatstone's bridge. The situation can be depicted as shown in figure. As resistances \[S\] and \[6\,\,\Omega \] are in parallel their effective resistance is                 \[\frac{6s}{6+S}\Omega \] As the bridge is balanced, hence it is balanced Wheatstone's bridge. For balancing condition,                 \[\frac{P}{Q}=\frac{R}{\left( \frac{6S}{6+S} \right)}\] or            \[\frac{2}{2}=\frac{2(6+S)}{6S}\] or            \[3S=6+S\] or            \[S=3\Omega \]