The Nernst equation is a fundamental equation in electrochemistry that relates the electrode potential of an electrode to the concentration of the electrolyte and the temperature. It is named after the German physicist Walther Nernst, who derived this equation in 1889.

The Nernst equation is given by:

E = E° - (RT/nF) * ln(Q)

where:
- E is the electrode potential
- E° is the standard electrode potential
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin
- n is the number of electrons involved in the redox reaction
- F is Faraday's constant (96,485 C/mol)
- Q is the reaction quotient, which is the ratio of the concentrations of the products to the concentrations of the reactants, each raised to the power of their stoichiometric coefficients.

The Nernst equation shows that the electrode potential of an electrode is influenced by both temperature and the concentration of the electrolyte. Let's break down each factor:

1. Temperature:
- The Nernst equation includes the term (RT/nF), which is related to the temperature.
- As the temperature increases, the value of (RT/nF) also increases, resulting in a larger contribution to the electrode potential.
- Therefore, the temperature has a direct effect on the electrode potential.

2. Concentration of electrolyte:
- The Nernst equation includes the natural logarithm of the reaction quotient Q.
- The reaction quotient depends on the concentrations of the products and reactants.
- As the concentration of the products increases or the concentration of the reactants decreases, the value of Q increases.
- The natural logarithm of a larger Q value results in a more positive contribution to the electrode potential.
- Therefore, the concentration of the electrolyte also affects the electrode potential.

Thus, it is clear that the Nernst equation considers both temperature and the concentration of the electrolyte in determining the electrode potential. Hence, the correct answer is option C: Both a and b.