The potential gradient is defined as the fall of potential per unit length of the potentiometer wire. Complete the circuit as shown in figure, and note the current from ammeter A.
Let L = length of potentiometer wire AB,
`epsilon` = emf of the battery used in the potentiometer wire circuit, R = resistance from resistance box used in circuit, r= resistance of the wire AB. Total resistance of the circuit = R +r
Current in potentiometer wire,
`i = epsilon/(R + r)`
Fall of potential across potentiometer wire
` = ir = ((epsilon)/(R+r))r`
`:.` Potential gradient `= ("fall of potential")/("length")`
` = ((epsilon)/(R+r))r/L`
