A cell can maintain a stable voltage across its plasma membrane even when no rapid electrical signal is occurring. This baseline voltage is the resting membrane potential.

It arises from two ingredients:

1. unequal ion concentrations across the membrane;
2. selective membrane permeability to those ions.

The Na$^+$/K$^+$ ATPase and other transport processes maintain concentration gradients over time. Ion channels then allow selected ions to move down their electrochemical gradients.

Why potassium often dominates

Many resting animal-cell membranes are much more permeable to K$^+$ than to Na$^+$ because they contain K$^+$-selective leak channels that are open at rest.

K$^+$ therefore tends to move the membrane potential toward its equilibrium potential $E_K$. If the membrane were permeable only to K$^+$, the resting voltage would approach $E_K$.

Real membranes conduct several ions, so the resting potential usually lies between their equilibrium potentials.

A useful approximate model treats each ion pathway as having a conductance $g_i$, a measure of how readily that pathway carries electrical current. Then

$$\boxed{V_{\rm rest}\approx\frac{\sum_i g_iE_i}{\sum_i g_i}}.$$

This shows that the resting voltage is pulled most strongly toward the equilibrium potentials of ions with the largest resting conductance.

Example

Suppose a simplified membrane has

$$E_K=-90\ \mathrm{mV},\qquad E_{Na}=+60\ \mathrm{mV}$$

and resting conductances

$$g_K=20g_{Na}.$$

Then

$$V_{\rm rest}\approx\frac{20(-90)+1(60)}{21}\ \mathrm{mV}\approx-83\ \mathrm{mV}.$$

The small Na$^+$ permeability makes the resting voltage less negative than $E_K$, but K$^+$ still dominates.

Pumps and channels play different roles

The Na$^+$/K$^+$ ATPase is electrogenic, so it contributes directly to membrane voltage, but its deeper role is to maintain the Na$^+$ and K$^+$ concentration gradients that make rapid electrical signaling possible. The instantaneous resting voltage is usually determined mainly by which ion channels are open and the gradients already present.

Thus a resting membrane potential is not a static charge painted onto a cell. It is a steady electrical state maintained by nonequilibrium ion gradients plus selective permeability.