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In a meter bride, null point is 20 cm, w...

In a meter bride, null point is `20 cm`, when theknown resistence `R` is shunted by `10 Omega` resistence, null point is found to be shifted by `10 cm` . Find the unknown resistence `X`.

Text Solution

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The correct Answer is:
A
`R/X=l/(100-l)`
`:. X=((100-l)/l)R`
or `X= ((100-20)/20)R=4R`
When known resistance `R` is shunted, its net resistance will decrease. Therefore, resistence parallel to this (i.e.P) should also decrease or its new null point length should also decrease or its new null point length should also decrease.
`:. (R')/X=(l')/(100-l')`
`=(20-10)/(100-(20-10))=1/9`
or `X = 9R'`
From eqs (i) and (ii), we have
`4R = 9R' =[(10R)/(10+R)]`
Solving this equation, we get
`R = (50)/4 Omega`
Now, from Eq. (i), the unknown resistance
`X = 4R=4((50)/4)`
or `X=50Omega`
`R` is resuntant of `R` and `10 Omega` in parallel.
`:. 1/(R')=1/(10)+1/(R)`
or `R'= (10R)/(10+R)`.
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