An unknown resistance X is to be determined using resistances `R_1, R_2 or R_3`. Their corresponding null points are A, B and C. Find which of the above will give the most accurate reading and why?
. `R= R_1 or R_2 or R_3`.

Answer

B

Explanation

KEY CONCEPT : At all null points the wheatstone bridge will
be balanced
`:. X/(r_1) = R/(r_2)`
`rArr X = R (r_1/r_2)`
where R is a constant `r_1 and r_2` are variable.
The maximum fractional
error is
`(DeltaX)/X = (Delta r_1)/r_1 + (Delta r_2)/r_2`
Here, `Deltar_1 = Deltar_2 = y` (say) then
For `(DeltaX)/X to be minimum `r_1 xx r_2` should be max
`[:. r_1 + r_2 = c (constt.)]`
Let `E = r_1 xx r_2`
`rArr E = r_1 xx (r_1-c)`
`:. (dE)/(dr_1) = (r_1-c) + r_1 = 0`
`rArr r_1 = c/2 rArr r_2 = c/2 rArr r_1 = r_2`
`rArr R_2` gives the most accureate value.
.