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,                 \[\frac{P}{Q}=\frac{R}{\left( \frac{6S}{6+S} \right)}\]                 \[or\frac{2}{2}=\frac{2(6+S)}{6S}\] \[or3\,S=6+S\] \[orS=3\,\Omega \]