Page 360 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 28] ELECTROMAGNETIC INDUCTION 345

Hence the current in the inductor at this time is
I = I 0 e −t/T = (1.5A)(0.22) = 0.33 A

SOLVED PROBLEM 28.18
The 0.2-H, 3- inductor of Prob. 28-16 is connected in series with another 0.2-H, 3- inductor, and the
combination is again connected to a 6-V battery of internal resistance 1 .(a) Find the time constant of
the new circuit and the final current. (b) If the battery is short-circuited so the current flows only through
the inductors until it dies away, find the new time constant.
(a) The total inductance and total resistance are, respectively,

L = L 1 + L 2 = 0.2H + 0.2H = 0.4H R = R 1 + R 2 + R 3 = 3 + 3 + 1 = 7
The time constant is therefore
L 0.4H
T = = = 0.057 s
R 7
The final current is
V 6V
I 0 = = = 0.86 A
R 7
The final current is smaller, and a longer time is required for it to develop.
(b) The total inductance and total resistance of the combination of the two inductors are, respectively,
L = 0.2H + 0.2H = 0.4H R = 3 + 3 = 6

The time constant is now
L 0.4H
T = = = 0.067 s
R 6
which is the same as for one of the inductors by itself when short-circuited, as in Prob. 28.17.

Multiple-Choice Questions

28.1. Upon which one or more of the following does the magnetic flux through a wire loop in a magnetic field depend?
(a) the area of the loop
(b) the shape of the loop
(c) the magnitude of the field
(d) the angle between the plane of the loop and the direction of the field

28.2. According to Lenz’s law an induced current
(a) gives rise to a magnetic field of its own that opposes the flux change that created it
(b) gives rise to a magnetic field of its own that reinforces the flux change that created it
(c) appears when a wire moves parallel to a magnetic field
(d) appears when a wire moves perpendicular to a magnetic field
28.3. The cause of the alternating current in the secondary coil of a transformer is an emf produced by

(a) the varying electric field of the primary coil
(b) the varying magnetic field of the primary coil
(c) the varying magnetic field of the secondary coil
(d) the voltage applied to the primary coil