In the figure a long uniform potentiometer wire AB is having a constant potential gradient along its length. The null points for the two primary cells of emfs `epsilon_(1) " and " epsilon_(2)` connected in the manner shown are obtained at a distance of 120 cm and 300 cm from the end A. Find (i) `epsilon_(1)//epsilon_(2)` and (ii) position of null point for the cell `epsilon_(1)`.
How is the sensitivity of a potentiometer increased ?

Explanation

In first combination `epsilon_(1) " and " epsilon_(2)` are opposing each other while in second combination `epsilon_(1) " and " epsilon_(2)` are adding each other, so,
`epsilon_(1)-epsilon_(2)=Kl_(1)`
`epsilon_(1)+epsilon_(2)=Kl_(2)`
`implies (epsilon_(1)-epsilon_(2))/(epsilon_(1)+epsilon_(2))=(l_(1))/(l_(2)) implies (epsilon_(1)-epsilon_(2))/(epsilon_(1)+epsilon_(2))=(120)/(300)`
`5 epsilon_(1)-5epsilon_(2)=2 epsilon_(1)+2epsilon_(2)`
`5 epsilon_(1)-2epsilon_(1)=2epsilon_(2)+5epsilon_(2)`
`implies 3 epsilon_(1)=7epsilon_(2) implies (epsilon_(1))/(epsilon_(2))=(7)/(3) implies epsilon_(1) : epsilon_(2)=7 : 3`
The sensitivity of a potentiometer can be increased by reducing the potential gradient.