^At balanced state

At balanced state

1. current in the galvanometer arm Ig is zero and

2. current flowing in the mesh ABCD is

3. Potential drop across AB is V = IRp

4. Potential gradient K = V/L

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

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

7. To get the null point within the length of the  potentiometer ξD > ξA

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 (ξA) but depends upon emf of driver cell (ξD), its internal resistance (rD), resistance of potentiometer wire (AB) & any resistance (R) in the main circuit. 

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