How does the resting membrane potential depend on ion concentrations?

Any voltage is a difference in electric potential between two points—for example, the separation of positive and negative electric charges on opposite sides of a resistive barrier. The typical resting membrane potential of a cell arises from the separation of potassium ions from intracellular, relatively immobile anions across the membrane of the cell. Because the membrane permeability for potassium is much higher than that for other ions (disregarding voltage-gated channels at this stage), and because of the strong chemical gradient for potassium, potassium ions flow from the cytosol into the extracellular space carrying out positive charge, until their movement is balanced by build-up of negative charge on the inner surface of the membrane. Again, because of the high relative permeability for potassium, the resulting membrane potential is almost always close to the potassium reversal potential. But in order for this process to occur, a concentration gradient of potassium ions must first be set up. This work is done by the ion pumps/transporters and/or exchangers and generally is powered by ATP.

In the case of the resting membrane potential across an animal cell's plasma membrane, potassium (and sodium) gradients are established by the Na+/K+-ATPase (sodium-potassium pump) which transports 2 potassium ions inside and 3 sodium ions outside at the cost of 1 ATP molecule. In other cases, for example, a membrane potential may be established by acidification of the inside of a membranous compartment (such as the proton pump that generates membrane potential across synaptic vesicle membranes).