question_answer

Three resistances P, Q, R each of \[2\Omega \] and an unknown resistance S form the four arms of a Wheatstones 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 :

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 Wheatstones 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            \[S=3\,\Omega \]