Calculate the resistance:

For Calculate the resistance R_x, a tapping key K is held down momentarily and the bridge is balanced through adjusting R₃ to get no deflection in galvanometer under these conditions.

Within the bridge the total current is divided within two paths: i₁ through R₁ and R₃, and i₂ through R₂ and R_x.  Under the balancing conditions, the potential at points B and D must be the similar, that is the ohmic voltage drop through the resistors R₁ and R₂ must be the same.  Therefore, the potential at B (E_B) must be equal to potential at D (E_D).

E_B = E_D                                                                       ... (1)

Or i₁ R₁ = i₂R₂                                                            ... (2)

Similarly, i₁ R₃ = i₂ R_x                                              ...  (3)

Dividing Equation (2) through Equation (3), we get

R₁ / R₃  = R₂/ R_X

and R_x  =       R₂  R₃/R₁                                                           ...  (4)

Thus, we could calculate R_x as R₁, R₂ and R₃ are all known. The Conductance G, being the reciprocal of resistance will be,

 G = R₁/R₂ R₃                ...  (5) 

the input potential, E_i, is balanced by the current from amplifier output which passes through a feedback resistor (R_f). The output potential, E₀ is in terms of resistance:

E₀ = E_i (R_f/R_x + 1)

here R_x is the resistance of conductometric cell.

With the respect to the solution conductance, G, above equation becomes

E₀ = E_i(R_fG + 1)

Figure: An operational amplifier control circuit for conductometric measurement.

Here R_x is the solution resistance and R_f is the feedback resistance