A potentiometer wire is 100 cm long and a constant potential difference is maintained across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at 64 cm and 32 cm from the positive end of the wire in the two cases. the ratio of emf's is

Options

A. `5:4`
B. `3:4`
C. `3:2`
D. `5:1`

Answer

C

Explanation

`3:2`
In helping condition `epsilon_(1) + epsilon_(2) prop l_(3)`
in opposing condition `epsilon_(1) - epsilon_(2) prop l_(4) " " [because epsilon_(1) gt epsilon_(2) ] `
`therefore (epsilon_(1) + epsilon_(2))/(epsilon_(1) - epsilon_(2)) = (l_(3))/(l_(4)) = (50)/(10) = (5)/(1) `
`(2 epsilon_(1))/(2 epsilon_(2)) = (5 + 1)/(5 - 1)`
`therefore (epsilon_(1) )/(epsilon_(2)) = (6)/(4) " " therefore (epsilon_(1))/(epsilon_(2)) = (3)/(2)`