M.F. of the dynamo. Then E1 is
proportional to the product of the angular velocity, and a certain
function of the current. For a velocity [omega], let this function be
denoted by _f_(C). If the characteristic of the dynamo can be drawn,
then _f_(C) is known.
We have then
w
E1 = -------- f
[Omega] (1.)
If R be the resistance in circuit by Ohm's law,
E - E1
C = --------
R
w
= E ------- f(C)
[Omega]
----------------
R
and therefore
[Omega](E - CR) (2.)
w = -----------------
f(C)
Let _a_ be the efficiency with which the motor transforms electrical
into mechanical energy, then--
Power required = L w = a E1 C
w
= a C ------- f(C)
[Omega]
Dividing by _w_,
a C f(C)
L = -------- . (3.)
[Omega]
It must be noted that L is here measured in electrical measure, or,
adopting the unit given by Dr. Siemens in the British Association
Address, in joules. One joule equals approximately 0.74 foot pound.
Equation 3 gives at once an analytical proof of the second principle
stated above, that for a given motor the current depends upon the
couple, and upon it alone. Equation 2 shows that with a given load the
speed depends upon E, the electromotive force of the main, and R the
resistance in circuit.
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