I have also
incidentally mentioned the fact that where rapidly varying currents
are employed, the strength of the electric current that a given
battery can yield is determined not so much by the resistance of the
electric circuit as by its electric inertia. It is not a very easy
task to explain precisely what happens to an electric circuit when the
current is turned on suddenly. The current does not suddenly rise to
its full value, being retarded by inertia. The ordinary law of Ohm in
its simple form no longer applies; one needs to apply that other law
which bears the name of the law of Helmholtz, the use of which is to
give us an expression, not for the final value of the current, but for
its value at any short time, t, after the current has been turned on.
The strength of the current after a lapse of a short time, t, cannot
be calculated by the simple process of taking the electromotive force
and dividing it by the resistance, as you would calculate steady
currents.
In symbols, Helmholtz's law is:
i_{t} = E/R ( 1 - e^{-(R/L)t} )
In this formula i_{t} means the strength of the current after the
lapse of a short time t; E is the electromotive force; R, the
resistance of the whole circuit; L, its coefficient of self-induction;
and _e_ the number 2.
Pages:
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85