^At balanced state

At balanced state

1. current in the galvanometer arm I_g is zero and

2. current flowing in the mesh ABCD is

3. Potential drop across AB is V = IR_p

4. Potential gradient K = V/L

5. As ξ_A is balanced against the potential drop of  length AN, thus

6. ξ_A ∝ b is called the principle of potentiometer.

7. To get the null point within the length of the  potentiometer ξ_D > ξ_A

Greater the length of the potentiometer wire (L), smaller is the potential gradient (k) & more is the balancing length (b), hence more is the accuracy. ‘k’ is independent of the emf of auxillary cell (ξ_A) but depends upon emf of driver cell (ξ_D), its internal resistance (r_D), resistance of potentiometer wire (AB) & any resistance (R) in the main circuit.