Voltage sources can be connected in series, to increase or decrease the total voltage applied to a system as shown in
Fig. 1. The net voltage is determined by summing the sources with the same polarity and
subtracting the total of the sources with the opposite polarity. The net polarity is the polarity of the larger sum.
Fig. 1: Voltage sources in series (same polarity).
Fig. 2: Voltage sources in series(different polarity).
In
Fig. 1, for example, the sources are all pressuring current to follow a clockwise path, so the net voltage is
$$E_T = E_1 + E_2 + E_3$$
$$E_T = 10 V + 6 V + 2 V = 18 V$$
In
Fig. 2, however, the 4 V source is "pressuring"
current in the clockwise direction while the other two are trying
to establish current in the counterclockwise direction. In this case, the
applied voltage for a counterclockwise direction is greater than that for
the clockwise direction. The result is the counterclockwise direction
for the current as shown in
Fig. 2. The net effect can be determined
by finding the difference in applied voltage between those supplies
"pressuring" current in one direction and the total in the other
direction. In this case,
$$E_T = E_1 + E_2 + E_3$$
$$E_T = 9 V + 3 V - 4 V = 8 V$$
with the polarity shown in the figure.
Example of Series Voltage Sources
The connection of batteries in series to obtain a higher voltage is common
in much of today's portable electronic equipment.
Fig. 3: Series and parallel combination of batteries.
For example, four 1.5 V AAA batteries have been connected in series to
obtain a source voltage of 6 V. Although the voltage has increased,
keep in mind that the maximum current for each AAA battery and for
the 6 V supply is still the same. However, the power available has
increased by a factor of 4 due to the increase in terminal voltage.
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