On interchanging the resistance , the balance point of a metre brige shifs to the left by 10 cm . The resistance of their series combination is `1kOmega` . How much was the resistance on the left slot before interchanging the resistance ?

Options

A. `500Omega`
B. `910Omega`
C. `990Omega`
D. `505Omega`

Answer

A

Explanation

The balance condition in the first case ,
`(R_(1))/(l)=(R_(2))/(100-l)`
or , `(R_(1))/(R_(2))=(l)/(100-l)" " ...(1)`

When the resistance `R_(1)andR_(2)` are interchanged in the second case ,
`(R_(1))/(R_(2))=(l-10)/(100-1(l-10))`
or , `(R_(1))/(R_(2))=(100-l)/(l-10)" " ...(2)`
From equation (1) and (2) we ge t ,
`(l)/(100-l)=(110-l)/(l-10)`
or, `l(l-10)=(100-l)(110-l)" or, "l=55"cm"`
Fromequation (1) we get ,
`R_(1)=(55)/(45)R_(2)`
Given , `R_(1)+R_(2)=1000`
`thereforeR_(1)=(55)/(45)(1000-R_(1))" or, "R_(1)=550Omega`