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Internal resistance

A practical electrical power source which is a linear electric circuit may, according to Thévenin's theorem, be represented as an ideal voltage source in series with an impedance. This resistance is termed the internal resistance of the source. When the power source delivers current, the measured e.m.f. (voltage output) is lower than the no-load voltage; the difference is the voltage (the product of current and resistance) drop caused by the internal resistance. The concept of internal resistance applies to all kinds of electrical sources and is useful for analyzing many types of electrical circuits.[1]


Batteries can be approximately modeled as a voltage source in series with a resistance. Internal resistance of a battery is dependent on the specific battery's size, chemical properties, age, temperature and the discharge current. Measurement of the internal resistance of a battery is a guide to its condition, but may not apply at other than the test conditions. Internal resistance depends upon temperature; for example, a fresh Energizer E91 AA alkaline primary battery drops from about 0.9 ohms at -40 °C to about 0.1 ohms at 40 °C.[2]

The internal resistance of a battery can be calculated from its open circuit voltage, voltage on-load, and the load current. An equivalent series resistance (ESR) meter as used to measure the ESR of capacitors, essentially an AC milliohmmeter, can be used.[3]

Internal resistance increases with the age of a battery, but for most battery types ranges from a fraction of an ohm to a few ohms.

In use the useful voltage produced by a disposable battery decreases until it drops so far that the battery must be discarded. This is largely due to an increase in internal resistance rather than a drop in the voltage of the equivalent source.

See also

Norton's theorem


^ Paul Horowitz, Winfield Hill, The Art of Electronics Second Edition, Cambridge University Press, 1989 ISBN 0-521-379095-7 p.12
^ "Battery Internal Resistance". Energizer Technical Bulletin. Energizer Battery. 200512.
^ Testing batteries with ESR meter

Student Reference Manual for Electronic Instrumentation Laboratories (2nd Edition) - Stanley Wolf & Richard F.M. Smith

Fundamentals of Electric Circuits (4th Edition) - Charles Alexander & Matthew Sadiku

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