# 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 voltage output is lower than the no-load voltage; the difference is the voltage drop (the product of current and resistance) 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.

## Batteries

Batteries can be approximately modeled as a voltage source in series with a resistance. The internal resistance of a battery is dependent on the specific battery's size, chemical properties, age, temperature and the discharge current. It has an electronic component due to the resistivity of the battery's component materials and an ionic component due to electrochemical factors such as electrolyte conductivity, ion mobility, and electrode surface area. Measurement of the internal resistance of a battery is a guide to its condition, but may not apply at other than the test conditions. Measurement with an alternating current, typically at a frequency of 1kHz, may underestimate the resistance, as the frequency may be too high to take into account the slower electrochemical processes. Internal resistance depends upon temperature; for example, a fresh Energizer E91 AA alkaline primary battery drops from about 0.9 ohms at -40 °C, where the low temperature reduces ion mobility, to about 0.15 ohms at room temperature and about 0.1 ohms at 40 °C.[1]

The internal resistance of a battery can be calculated from its open circuit voltage, voltage on-load, and the load resistance:

$R_{\text{int}} = ({\frac{ V_{\text{NL}} } { V_{\text{FL}} } - 1 } ) { R_{\text{L}} }$


Many equivalent series resistance (ESR) meters, essentially AC milliohmmeters normally used to measure the ESR of capacitors, can be used to estimate battery internal resistance, particularly to check the state of discharge of a battery rather than obtain an accurate dc value.[2] Some chargers for rechargeable batteries indicate the ESR.

In use the voltage across the terminals of a disposable battery driving a load decreases until it drops too low to be useful; this is largely due to an increase in internal resistance rather than a drop in the voltage of the equivalent source.

With rechargeable lithium polymer batteries the internal resistance is largely independent of the state of charge, but increases as the battery ages, thus is a good indicator of expected life.[3][4]