Question

State the principle of a potentiometer. Define potential gradient. Obtain an expression for potential gradient in terms of resistivity of the potentiometer wire.

Answer 1

Principle
When a constant current is passed through a wire of uniform area of cross-section, the potential drop across any portion of the wire is directly proportional to the length of that portion.
Let V be the potential difference across certain portion of the wire, whose resistance is R. If I is the current through the wire, then \[V = IR\] We know that \[R = \rho\frac{l}{A}\], where l, A and ρ are length, area of cross-section and resistivity of the material of the wire, respectively.

\[\therefore V = I\rho\frac{l}{A}\]

\[ \Rightarrow \frac{V}{l} = \frac{I\rho}{A}\]