In an experiment to measure the internal resistance of a cell by a potentiometer, it is found that the balance point is at a length of `2 m` when the cell is shunted by a `5 Omega` resistance and is at a length of `3 m` when the cell is shunted by a `10 Omega` resistance, the internal resistance of the cell is then

Options

A. `1.5 Omega`
B. `10 Omega`
C. `15 Omega`
D. `1 Omega`

Answer

A, B

Explanation

Acceleration of A,B,C are `a_(1),a_(2),a_(3)` upwards respectively.
Same string implies same tension.
String constraint : `a_(2)-2a_(3)-2a_(1)-2a_(2)+a_(1)=0 " or" -a_(2)-a_(2)-2a_(3)=0`
`a_(1)+a_(2)+2a_(3)=0`
For B : `T-mg =ma_(2)`
For A : `T-mg = ma_(1)`
For `C : 2T - mg = ma_(3)`
`a_(1)=a_(2)=-a_(3)`
`T-mg =- (2T-mg)`
`3T = 2mg`
`T = (2mg)/(3)`