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Physics LibreTexts

6.2.1: Electromotive Force and Internal Resistance

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The reader is reminded of the following definition from section 4.1:

Definition. The potential difference across the poles of a cell when no current is being taken from it is called the electromotive force (EMF) of the cell.

I shall use the symbol E for EMF.

Question. A 4 Ω resistance is connected across a cell of EMF 2 V. What current flows?

The immediate answer is 0.5 A – but this is likely to be wrong. The reason is that a cell has a resistance of its own – its internal resistance. The internal resistance of a lead-acid cell is typically quite small, but most dry cells have an appreciable internal resistance. If the external resistance is R and the internal resistance is r, the total resistance of the circuit is R+r, so that the current that flows is E/(R+r).

Whenever a current is taken from a cell (or battery) the potential difference across its poles drops to a value less than its EMF. We can think of a cell as an EMF in series with an internal resistance:

IV.4.png
FIGURE IV.4

If we take the point A as having zero potential, we see that the potential of the point B will be E - Ir, and this, then, is the potential difference across the poles of the cell when a current I is being taken from it.

Show that this can also be written as ERR+r.


This page titled 6.2.1: Electromotive Force and Internal Resistance is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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