32 ELEMENTS OF ELECTRICAL ENGINEERING

line similar also to that of the current, as shown in Fig. 11 as <$.
The e.m.f. generated hereby is proportional to the change of
iLj and is thus a maximum where iL changes most rapidly, or at
its zero point, and zero where iL is a maximum, and according
to Lentz's law it is positive during falling and negative during
rising current. Thus this generated e.m.f. is a wave following f

the wave of current by the time t = -A >
1

where to is time of one
complete period, = -v or by the time angle 6 = 90°.

FIG. 11.—Self-induction effects produced by an alternating sine wave

of current.

This e.m.f. is called the counter e.m.f. of inductance. It is
e/ = - L di

= — 2 TT/L/O cos 2 irft.

It is shown in dotted line in Fig. 11 as eV
The quantity 2 wfL is called the inductive reactance of the
circuit, and denoted by x. It is of the nature of a resistance,
and expressed in ohms. If L is given in 109 absolute unite or
henrys, x appears in ohms.

The counter e.m.f. of inductance of the current, i = Jo sin
2 irft = Jo sin 0, of effective value

r L .

I = -.....~;r> IS

•V/2

e\ = — x!Q cos 2 irft = — #Io cos ^,
having a maximum value of X!Q and an effective value of