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

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

Text Solution

Verified by Experts

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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