At the electrode surface, the redox reaction occurs:

. The reaction rates of the forward direction

and backward direction

depend on the applied potential

at the electrode:

,

,

where

(in V) is the standard potential of the redox reaction,

(in V) is the applied potential,

is the gas constant (

J/K mol),

is the Faraday constant (

C/mol),

(in K) is the temperature,

is the number of electrons transferred,

is the standard heterogeneous rate constant (in m/s), and

is the transfer coefficient (

in this case).

The net current at the electrode is the sum of the currents in the forward (cathodic current) and backward directions (anodic current).

Then

, where

(m

) is the surface area of the electrode, [Ox] and [Red] are the concentrations of the oxidant and reductor, and, replacing

and

, we have

.

This is called the Butler–Volmer equation, the fundamental relationship between current and applied potential.

This Demonstration shows that

and

change rapidly when the potential differs significantly from the standard potential

. When the standard rate constant

is very large, the current changes rapidly near the standard potential and the system is in a reversible state. When

is small, the system is in an irreversible state.