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ciated with the applied ac signal may put the coil at or near saturation,
and the resulting inductance level for the applied ac signal will be significantly
less than expected. You will find that the maximum dc current
is normally provided in supply manuals and data sheets to ensure avoidance
of the saturation region.
Equation (12.4) also reveals that the larger the inductance of a coil
(with N fixed), the larger will be the instantaneous change in flux
linking the coil due to an instantaneous change in current through the
coil.
If we write Eq. (12.1) as
df df di
eL � N � ��N � �
dt
di �� dt�
and substitute Eq. (12.4), we then have
eL � L � di
�
dt
(V) (12.5)
revealing that the magnitude of the voltage across an inductor is directly
related to the inductance L and the instantaneous rate of change of current
through the coil. Obviously, therefore, the greater the rate of
change of current through the coil, the greater will be the induced voltage.
This certainly agrees with our earlier discussion of Lenz’s law.
When induced effects are employed in the generation of voltages
such as those available from dc or ac generators, the symbol e is appropriate
for the induced voltage. However, in network analysis the voltage
across an inductor will always have a polarity such as to oppose the
source that produced it, and therefore the following notation will be
used throughout the analysis to come:
vL � L � di
�
dt
(12.6)
If the current through the coil fails to change at a particular instant,
the induced voltage across the coil will be zero. For dc applications,
after the transient effect has passed, di/dt � 0, and the induced voltage
is
di
vL � L � � L(0) � 0 V
dt
Recall that the equation for the current of a capacitor is the following:
dvC iC � C �
dt
Note the similarity between this equation and Eq. (12.6). In fact, if we
apply the duality v i (that is, interchange the two) and L C for
capacitance and inductance, each equation can be derived from the
other.
The average voltage across the coil is defined by the equation
vLav � L � Di
�
Dt
(V) (12.7)
INDUCED VOLTAGE ⏐⏐⏐ 479