Page 357 - Schaum's Outline of Theory and Problems of Applied Physics

342 ELECTROMAGNETIC INDUCTION [CHAP. 28

Fig. 28-5

equal IR by Ohm’s law:
I
V − L = IR
t
Impressed voltage − induced emf = net voltage

The rate of increase of the current at the moment when the current is I is accordingly
I V − IR
=
t L
The larger the inductance L, the more gradually the current increases. When the switch is first closed, I = 0 and
I V
=
t L
Eventually the current stops rising and I/ t = 0. From then on
V
I =
R
The final current depends only on V and R; the effect of L is to delay the establishment of the final current.
As shown in Fig. 28-6, the current in the circuit of Fig. 28-5 rises gradually in such a manner that after a
time t equal to L/R it reaches 63 percent of its final value. The quantity L/R is called the time constant T of the
circuit; the smaller the time constant, the more rapidly the current changes.
The formula that governs the growth of a current in the circuit of Fig. 28-5 is
I = I 0 (1 − e −t/T )

Fig. 28-6