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.