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 impedance 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.

A battery may be modeled as a voltage source in series with a resistance. In practice, the internal resistance of a battery is dependent on its size, chemical properties, age, temperature, and the discharge current. It has an electronic component due to the resistivity of the 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 7003100000000000000♠1 kHz, may underestimate the resistance, as the frequency may be too high to take into account slower electrochemical processes. Internal resistance depends on temperature; for example, a fresh Energizer E91 AA alkaline primary battery drops from about 0.9 Ω at -40 °C, when the low temperature reduces ion mobility, to about 0.15 Ω at room temperature and about 0.1 Ω at 40 °C.

The internal resistance of a battery may be calculated from its open circuit voltage V_NL, load voltage V_FL, and the load resistance R_L:

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

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