Re: emf, potential, voltage

["John S. Denker" <jsd@MONMOUTH.COM>]

At 01:18 PM 3/13/01 -0600, RAUBER, JOEL wrote:
> Why do books sometimes refer to the emf (or back emf) of an inductor or
> capacitor and not for a resister. i.e. is there something different about
> the voltage that one measures across a capacitor or an inductor or battery
> compared to other measurement such as one across a resistor.

Here's the deal:

1) As a point of terminology: I consider "emf" and "voltage" to be
essentially synonymous.

2) Let's consider the physics of a two-terminal black box containing a
linear circuit (perhaps some network of batteries and resistors).  The
two-terminal properties of the black box can by understood by looking at
the current-versus-voltage graph.  It's a straight line.

                |
               \|
                \
                |\
                | \
        current |  \
                |   \
                |    \
                |_____\_______
                       \    voltage


  a) Two points determine a line.  Consider the places where the line
crosses the axes in the graph above.  These are called the open-circuit
voltage and the short-circuit current.  If we know these two numbers, we
can draw a straight line and know the entire I-V curve.
  b) A point and a slope determine a line.  If we know the open-circuit
voltage and the impedance, we can draw a straight line and know the entire
I-V curve.  This gives rise to the Thevenin equivalent circuit0.
  c) A point and a slope determine a line.  If we know the short-circuit
current and the impedance, we can draw a straight line and know the entire
I-V curve.  This gives rise to the Norton equivalent circuit.

3) The same ideas apply to AC circuits.  We can have an AC open-circuit
voltage and an AC short-circuit current.

4) Suppose I have a motor, and I apply 115V(AC RMS) to its terminals.  Then
the average emf across its terminals is 115V.  That tells me the emf, not
the back emf.  If I measure the current under these conditions, that gives
me one point on the I-V curve.  Call this point (V1,I1).  One point is not
enough;  I need another point in order to pin down the first-order
properties of this device.

To get a second data point, I briefly open-circuit the terminals.  The
still-spinning motor will act like a generator.  It will produce a certain
voltage (i.e. emf) on its terminals.  This is the open-circuit
voltage.  Call this point (V0,I0) where I0=0 and V0 is called the "back emf".

Given these two points, (V1,I1) and (V0,I0), we can draw a straight line
and have a nice first-order model of the behavior of the device.

======

To answer Joel's question:  yes, there is something special about a
resistor as opposed to a motor, inductor, capacitor, or battery:  The
resistor is the only one of these that cannot (by itself) exhibit a back
emf, because it cannot store energy and cannot transfer energy from an
external source into our linear circuit.

(Resistors transferring energy to a _non_linear circuit are another matter
entirely.)

Do not confuse "back emf" with plain old "emf".