286 Aptitude Test Problems in Physics
inductance is determined only by geometrical con-
figuration and the number of turns of the coil (we
speak of long cylindrical coils with uniform wind-
ing). Let us derive this relation.
From the superposition principle for a magnetic
field, it follows that the magnetic field produced
by a current I in a coil of a given size is proportional
to the number of turns in it. Indeed, the doubling
of the number of turns in the coil can be treated as
a replacement of each turn by two new closely
located turns. These two turns will produce twice
as strong a field as that produced by a single turn
since the fields produced by two turns are added.
Therefore, the field in a coil with twice as many
turns is twice as strong. Thus, B (X N (B is the
magnetic induction, and the current is fixed).
It should be noted that the magnetic flux embraced
by the turns of the coil is
41) = BNS oc BN cc N 2.It remains for us to consider thatL=— (X N 2.
Thus, we obtain L = kN 2 for a given geometry.
Further, we take into account that N 1 =
N2 = YL2/k, and hence L = k (N 1 + N 3 ) 2. Con-
sequently,L = Li + La + 2 1lLIL 2.3.57. For a motor with a separate excitation, we
obtain the circuit shown in Fig. 224. In the first
case, i.e. when the winch is not loaded, 0 = / 1 =
OS — W 1 )/r, where r is the internal resistance of
the motor, and is the induced emf, =
Thus, 16^1 = 15, whence a = Vv 1. In the second
case, the power consumed by the motor isOS —WO W2
21 2 =^ MgV2.