question_answer

In Wheatstones network \[P=2\Omega ,\,Q=2\Omega ,\,R=2\Omega \]and\[S=3\Omega \]. The resistance  with which S is to shunted in order that the bridge may be balanced is

A)  \[2\Omega \]   

B)  \[6\Omega \]

C)  \[1\Omega \]  

D)  \[4\Omega \]

Correct Answer: B

Solution :

: Let X be the resistance with which S is to be shunted for the bridge to be balanced.                 Then, for balanced Wheatstones bridge \[\frac{P}{Q}=\frac{R}{\frac{SX}{S+X}}\](\[\because \] S and X are in parallel) Substituting the given values, we get \[\frac{2\Omega }{2\Omega }=\frac{2\Omega }{\frac{(3\Omega )X}{3\Omega +X}}\] or \[\frac{(3\Omega )X}{3\Omega +X}=2\Omega \] \[(3\Omega )X=(2\Omega )(3\Omega )+(2\Omega )X\] \[X(3\Omega -2\Omega )=(2\Omega )\,(3\Omega )\] \[X(1\,\Omega )=(2\Omega )\,(3\Omega )\] \[X=\frac{(2\Omega )\,\,(3\Omega )}{1\Omega }=6\Omega \]