question_answer

In metre-bridge the balancing length from left is found to be 20 cm when standard resistance of \[1\,\,\Omega \] is in right gap. The value of unknown resistance is:                                                                                               [AIPMT 1999]

A)  \[0.25\,\,\Omega \]        

B)       \[0.4\,\,\Omega \]

C)  \[0.5\,\,\Omega \]          

D)       \[4\,\,\Omega \]

Correct Answer: A

Solution :

[a] Let unknown resistance be X.

Then condition of Wheatstone's bridge gives, \[\frac{X}{R}=\frac{20\,r}{80\,r}\]

Hence, unknown resistance is

\[X=\frac{20}{80}\times R=\frac{1}{4}\times 1\] \[(\because \,R=1\,\Omega )\]

\[=0.25\,\Omega \]