**Core Concept**
The equilibrium potential, also known as the Nernst potential, is a measure of the electrical potential difference that would occur if a specific ion were the only ion moving across a cell membrane. It is an important concept in understanding how ions influence the resting membrane potential.

**Why the Correct Answer is Right**
The equilibrium potential is calculated using the Nernst equation, which takes into account the ion's concentration gradient, temperature, and the ion's valence (charge). The Nernst equation is given by:

E = (RT/F) * ln([ion outside]/[ion inside])

where E is the equilibrium potential, R is the gas constant, T is the temperature in Kelvin, F is Faraday's constant, and [ion outside] and [ion inside] are the concentrations of the ion outside and inside the cell, respectively. This equation shows that the equilibrium potential is directly related to the ratio of the ion concentrations outside and inside the cell.

**Why Each Wrong Option is Incorrect**

**Option A:** This option is incorrect because the Goldman-Hodgkin-Katz equation, while related to the equilibrium potential, is a more complex equation that takes into account the movement of multiple ions across the membrane, whereas the Nernst equation is specific to a single ion.

**Option B:** This option is incorrect because the electrochemical gradient is a broader concept that encompasses not only the concentration gradient but also the electrical gradient, whereas the equilibrium potential is a specific measure of the electrical potential difference.

**Option C:** This option is incorrect because the resting membrane potential is the actual electrical potential difference across the cell membrane, whereas the equilibrium potential is a theoretical value that represents the electrical potential difference that would occur if a specific ion were the only ion moving across the membrane.

**Clinical Pearl / High-Yield Fact**
The Nernst equation is a powerful tool for understanding how ions influence the resting membrane potential, and it has important implications for understanding a wide range of physiological and pathological processes, including the regulation of nerve and muscle function.

**Correct Answer:** C. The Goldman-Hodgkin-Katz equation is actually the one that is used to calculate the resting membrane potential, not the equilibrium potential, which is calculated using the Nernst equation.