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Internal Resistance

<^< Examples: Batteries | Course Index | Examples: Internal Resistance >^>(:nl:)

All sources of voltage (or e.m.f.) have a certain amount of resistance inside them. This resistance limits the amount of current that a source of voltage can supply. Because the resistance appears to be inside the voltage source we refer to it as "internal resistance".

With a large battery, such as a 12V lead-acid car battery, the internal resistance is very small (typically a fraction of an ohm). On the other hand, a small 1.5V dry cell will usually have an internal resistance of a few ohms. Like the lead-acid battery, this resistance increases as the battery becomes exhausted (or goes "flat").

Because we can't actually see the resistance (remember that it's hidden inside the voltage source) this doesn't mean that it's unimportant. If we need a voltage source that can deliver a large value of current we need to ensure that its internal resistance is as small as possible. A perfect voltage source would have zero internal resistance.

To consider the effect of internal resistance on the output voltage of a real battery, we can think of the battery as being a perfect voltage source connected in series with a resistor equal to its internal resistance, as shown in the diagram.

The voltage that appears at the battery terminals is less than the voltage produced by the voltage source by an amount equal to the voltage dropped across the internal resistance. Hence the output voltage produced by the battery when connected to a load of R ohms is given by:

V'_OUT_' = V - (I x R'_S_') where I is the current flowing in the load, and R'_S_' is the internal resistance.

Finally, it's worth noting that, when a battery is not supplying any current at all (i.e. when no load is connected to it), its terminal voltage, V'_OUT_', will be the same as its internal voltage, V. However, when a load is connected to the same battery (and current is drawn from it) its terminal voltage will fall. (:nl:)(:table style="clear:both":)