Explain the principle of a potentiomater.

Explanation

Principle of a potentiometer : The potential difference across any length of a potentiometer wire is directly proportional to that length. field
Explanation: The potentiometer consists of a long uniform wire AB of length L, stretched on a wooden board. A cell of constant emf E is connected across AB, as shown in the figure.

As the steady current passes through the wire from A to B, there is a tall of potential along the wire from A to B. As the wire has a uniform cross section, its resistance per unit length `lamda` is constant. Hence, the resistance of the wire is `Llamda` Therefore, the potential difference (p.d.) across the wire is
`V_(AB)="current"xx "resistance"=ILlambda`
`therefore I=V(V_AB)/(L lamda)`
Let P be any point of the wire between A and B. Let AP-L Then the resistance of the wire AP is 2. The p.d. between A and P is
`V_(AP)="current" xx "resistance of AP"=Illambda`
where `=(V_(AB))/(L)=k` (constant), as `V_(AB) and L` are constants.
The quantity k represents the fall of potential per unit length of the wire, which is called the potential gradient along the wire.
`therefore V_(AP)=kl therefore V_(AP) alpha l`
Thus, the p.d. across any length of the potentiometer wire is directly proportional to that length.