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In a Wheatstone's network, P=2Omega, Q=2...

In a Wheatstone's network, `P=2Omega, Q=2Omega, R=2Omega and S=3Omega`. The resistance with which S is to be shunted in order that the bridge may be balanced is

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The correct Answer is:
6
Let a resistance r `Omega` be shunted with resistance S, so that the bridge is balanced.
Let S. be the resultant resistance of S and r, then
In balanced position

`(P)/(Q) =(R )/(S.)`
`(2)/(2) =(2)/(S.)`
`:.S.=2Omega`
Now,
`(1)/(S.) =(1)/(S) +(1)/(r )`
`(1)/(r )=(1)/(S.) -(1)/(S) = (1)/(2)-(1)/(3) =(3-2)/(6)`
`(1)/(r )= (1)/(6)`
`r=6Omega`
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