question_answer

Three resistances P, Q, R each of \[2\,\Omega \] and an unknown resistance S form the four arms of a Wheat stone'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 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            \[S=3\Omega \]