Series Voltage Sources

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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