Principles:
A current, I, flows continuously from the battery through AB, causing a potential drop among A and B. From Ohm's law, this is given by:
EAB = IRAB ... (2.5)
The current passing among A and C is also I and is given by the potential drop between A and C
EAC = IRAC ... (2.6)
Resistance along resistor is linear. The given above could also be written as
EAB = IRAB = kI.AB .... (2.7)
EAC = IRAC = kI.AC .... (2.8)
Dividing (2.8) by (2.7) and rearranging,
EAC = EAB AC/ AB .... (2.9)
Now there are three possibilities exist if the potential divider is adjusted to a position of EAC and the key K is pressed. There are two of these that are when EAC is greater than EX (unknown potential) or Es (potential of standard cell) electrons will be forced to flow from right to left through the unknown cell and the direction will be reversed if EAC is less than Ex. The third case is where EAC is equal to Ex , and for this situation no current flows through the galvanometer and galvanic cell. However, electrons will continue to flow through AB under these circumstances. In practice the key is tapped and C is moved until the galvanometer indicates no current flow. When this balance is found, the position on voltage divider is noted say ACs. Similarly position on voltage divider with standard cell is also noted say ACs.
With the standard cell and the unknown cell in the circuit, Equation 2.9 becomes
ES = E ACs = EAB (ACs / AB) ... (2.10)
Ex = E = EAB AC x /AB ... (2.11)
where ACS and ACX represent the linear distances corresponding to balance point for the two cases. By Dividing these two equations and rearranging, we get
Ex = ES (AC x /ACS) ... (2.12)
Therefore Ex, the unknown potential of the cell, will be obtained by measuring the two distances with cell of unknown potential and the known emf of standard cell.