Consider the MB shown in the diagram, let the resistance X have temperature coefficient `alpha_(1)` and the resistance from the RB have the temperature coefficient `alpha_(2)`. Let the reading of the meter scale be 10 cm from the LHS. if the temperature of the two resistance increase by small temperature `DeltaT` then what is the shift in the position of the null point ? Neglect all the other changes in the bridge due to temperature rise.

Options

A. `9(alpha_(1)- alpha_(2))Delta T`
B. `9(alpha_(1)+alpha_(2))Delta T`
C. `1//9(alpha_(1) + alpha_(2))Delta T`
D. `1//9(alpha_(1)-alpha_(2))Delta T`

Answer

A

Explanation

`(X)/(10)=(90)/(90)rArr X=10Omega`
`rArr (10(1+alpha_(1)DeltaT))/(10+Deltal)=(90(1+alpha_(2)DeltaT))/(90-Deltal)`
`rArr(1+alpha_(1)DeltaT)(1+(Deltal)/(10))^(-1)=(1+alpha_(2)DeltaT)(1-(Deltal)/(90))`
`rArr (1+alpha_(1)DeltaT)(1-(DeltaT)/(10))=(1+alpha_(2)DeltaT)(1+(Deltal)/(90))`
`rArr1+alpha_(1)DeltaT-(Deltal)/(10)=1+alpha_(2)DeltaT+(Deltal)/(90)`
`rArr(alpha_(1)-alpha_(2))DeltaT=(Deltal)/(9)rArrDeltal=9(alpha_(1)-alpha_(2))DeltaT`