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 \[S=3\Omega \]