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Concept Version 8
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Charging a Battery: EMFs in Series and Parallel

When voltage sources are connected in series, their emfs and internal resistances are additive; in parallel, they stay the same.

Learning Objective

  • Compare the resistances and electromotive forces for the voltage sources connected in the same and opposite polarity, and in series and in parallel


Key Points

    • Emfs connected in the same polarity in series are additive and result in a higher total emf.
    • Two emfs connected in the opposite polarity in series have a total emf equal to the difference between them, and can be used to charge the lower voltage source.
    • Two voltage sources with identical emfs connected in parallel have a net emf equivalent to one emf source, however, the net internal resistance is less, and therefore produces a higher current.

Terms

  • series

    A number of things that follow on one after the other or are connected one after the other.

  • electromotive force

    (EMF)—The voltage generated by a battery or by the magnetic force according to Faraday's Law. It is measured in units of volts, not newtons, and thus, is not actually a force.

  • parallel

    An arrangement of electrical components such that a current flows along two or more paths.


Full Text

When more than one voltage source is used, they can be connected either in series or in parallel, similar to resistors in a circuit. When voltage sources are in series facing the same direction, their internal resistances add and their electromotive force, or emf, add algebraically. These types of voltage sources are common in flashlights, toys, and other appliances. Usually, the cells are in series in order to produce a larger total emf .

Flashlight and Bulb

A series connection of two voltage sources in the same direction. This schematic represents a flashlight with two cells (voltage sources) and a single bulb (load resistance) in series.

A battery is a multiple connection of voltaic cells. The disadvantage of series connections of cells in this manner, though, is that their internal resistances add. This can sometimes be problematic. For example, if you placed two 6v batteries in your car instead of the typical 12v single battery, you would be adding both the emfs and the internal resistances of each battery. You would therefore end up with the same 12v emf, though the internal resistance would then be doubled, causing issues for you when you want to start your engine.

But, if the cells oppose one another—such as when one is put into an appliance backwards—the total emf is less, since it is the algebraic sum of the individual emfs. When it is reversed, it produces an emf that opposes the other, and results in a difference between the two voltage sources .

Battery Charger

This represents two voltage sources connected in series with their emfs in opposition. Current flows in the direction of the greater emf and is limited by the sum of the internal resistances. (Note that each emf is represented by script E in the figure. ) A battery charger connected to a battery is an example of such a connection. The charger must have a larger emf than the battery to reverse current through it.

When two voltage sources with identical emfs are connected in parallel and also connected to a load resistance, the total emf is the same as the individual emfs. But the total internal resistance is reduced, since the internal resistances are in parallel. Thus, the parallel connection can produce a larger current .

Two Identical EMFs

Two voltage sources with identical emfs (each labeled by script E) connected in parallel produce the same emf but have a smaller total internal resistance than the individual sources. Parallel combinations are often used to deliver more current.

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