JeffM said:

Electromotive FORCE, actually.

Force

----- = pressure

area

Electricity has no analogous equivalent for pressure.

Voltage is a 'potential function'. It is a scalar function of position.

Force, on the other hand, is a vector function of position.

If you think of a wire, and a voltage difference along the wire, you can

see that the electric field is really being directed along the wire. So,

if you take a charge, and move it along the wire from one point to

another point, you'll do work on that charge because of the force

imparted on the charge by the field. The amount of work you do will be

the energy required. However, this amount of energy depends on the

amount of charge you move. More charge = more force. Thus, by dividing

out the amount of charge you used, you get a value which is independent

of the amount of charge. This is the voltage.

It's formally defined as the negative of the path integral of the

electric field between any two points. Since the electric field is

simply the vector equal to force on a charge divided by the charge, it's

easy to see that voltage is really just the difference in potential

energy, divided by the charge used to measure the energy. It's units are

joules/coulomb, which makes sense.

As far as analogies go, you think of the electric field as being like

the acceleration of gravity. Gravity is a vector field, pointing

downwards (the gravitational field). The resultant force on an object is

the field at that point, times the mass of that object. The 'voltage'

between two points, in this domain, would be the path integral of the

field (ie, acceleration of gravity) along the path between those two

points. In the gravitational realm, voltage is thus simply the

difference in height times a constant (assuming a constant gravitational

field). Given the right units, it would just be difference in height.

The potential energy difference between these two heights is the mass of

the object times this potential difference. Letting an object fall

through this height will give you a corresponding amount of kinetic energy.

Thus, voltage is neither pressure nor force. It's a way to predict the

amount of work you can get from an electric field.

The water analogy is that the electric field is like gravity, charge is

like mass, the rate of change of mass along some path is current, and

voltage is the difference in height between different pools. Voltage

differences don't make the mass want to move; it's paths along the

gravity vector that makes water move. Resistance is flow restriction of

the path. Power obtainable is head (which is height) * flow rate. etc, etc.