Current Electricity
9.0 Potentiometer
9.1 Comparison of emfs of two primary cells.
9.2 Determination of Internal resistance of a cell using potentiometer
9.0 Potentiometer
9.2 Determination of Internal resistance of a cell using potentiometer
It is a device which is mainly used to compare the emfs of two cells and to determine internal resistance of cell.
Construction
It consists of a long uniform wire $AB$ stretched in 4 to 10 segment. Each segment is of one metre length. The segments are stretched parallel to each other on a wooden board and the ends of wire are fixed to copper strips. A metre scale is fixed parallel to wire. The end $A$ is connected to the battery and end $B$ is connected to rheostat $(Rh)$.
Principle
When a constant current flows through a wire of uniform cross-sectional area, the potential drop across any length of the wire is directly proportional to that length.
Proof
When a jockey is made to touch a point $j$ on the wire, potential difference $(V)$ across the length of the wire $AJ$ is measured.
By ohm's law, $$V = IR \Rightarrow V = I\rho \frac{l}{A}$$
For a wire of uniform cross-section,resistivity $(\rho) $ and area of cross-section $A$ are constants.
When steady current $I$ flows through wire, $$ \Rightarrow \frac{{I\rho }}{A} = k = {\text{constant}}$$
Hence, $V = kl$ or $$V = kl\quad or\quad V \propto l$$
Potential gradient
The potential drop per unit length of potentiometer wire is known as a potential gradient. $$k = \frac{V}{l}$$
SI unit $V{m^{ - 1}}$
