If a circuit has more than one voltage source in series, then the voltage
sources may effectively be replaced by a single source having a value that is
the sum or difference of the individual sources. Since the sources may have
different polarities, it is necessary to consider polarities in determining the
resulting magnitude and polarity of the equivalent voltage source.
If the polarities of all the voltage sources are such that the sources
appear as voltage rises in given direction, then the resultant source is determined
by simple addition, as shown in Figure 5–15.
If the polarities of the voltage sources do not result in voltage rises in the
same direction, then we must compare the rises in one direction to the rises
in the other direction. The magnitude of the resultant source will be the sum
of the rises in one direction minus the sum of the rises in the opposite direction.
The polarity of the equivalent voltage source will be the same as the
polarity of whichever direction has the greater rise. Consider the voltage
sources shown in Figure 5–16.
If the rises in one direction were equal to the rises in the opposite direction,
then the resultant voltage source would be equal to zero.