Principle: The potentiometer is based upon the principle that when a constant current is passed through a wire of uniform area of cross-section, the potential drop across any portion of wire is directly proportional to the length of that portion.
Let V be potential difference across certain portion of 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 specific resistance of the material of wire respectively.
∴ V = Iρ\(\frac{l}{A}\)
If constant current is passed through the wire of uniform area of cross-section, then ρ, I and A are constants and we have
V = (constant) l
or V ∝ l
Hence, if a constant current flows through a wire of uniform area of cross-section, then potential drop along the wire is directly proportional to the length of the wire.
(a) Drift Velocity: It is the average velocity of the free electrons with which they get drifted towards the positive terminal under the influence of the external field.
Significance: The net current flowing through any cross-section is controlled by drift velocity and there is no transport of charges in a direction perpendicular to the applied field.
Relaxation Time (τ): The average time between successive collisions of electrons or ions in a conductor is called relaxation time.
Significance: It determines the drift velocity acquired by the electrons under the given applied electric force and also determines the electrical conductivity of a conductor at different temperatures.
(b) In first case:
vd = \(\frac{eV}{mL}\tau\)
In second case:
v'd = \(\frac{eV\tau}{m5L}\)
v'd = \(\frac{1}{5}(\frac{eV}{mL}\tau)\) = \(\frac{v_d}{5}\)
Thus we find that the drift velocity becomes \(\frac{1}{5}\) of its original value.
