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? [AIPMT (S) 2007]

A)              \[2\,\,\Omega \]

B)                   \[3\,\,\Omega \]

C)              \[6\,\,\Omega \]

D)                   \[1\,\,\Omega \]

Correct Answer: B

Solution :

[b] 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         \[3\,S=6+S\]

or         \[S=3\,\Omega \]