Understanding Battery Internal Resistance
Every electrochemical cell behaves as more than just an ideal voltage source. Inside the casing, ions migrate through electrolytes and electrons traverse conductive plates, and these motions are subject to restrictions. Those restrictions manifest as an opposition to current flow known as internal resistance. When a load is connected, part of the source voltage drops across this internal opposition rather than the external circuit, leading to reduced terminal voltage and wasted energy in the form of heat. Internal resistance is therefore a key indicator of a battery's health and suitability for high-drain applications. A fresh high-capacity cell exhibits only a tiny voltage drop under load, while an aged or damaged cell sags markedly even at moderate currents. Measuring this parameter enables engineers and hobbyists to predict performance, compare chemistries, and spot deteriorating cells before they fail unexpectedly.
The concept of internal resistance emerges from the Thevenin equivalent model of a battery: an ideal voltage source in series with a small resistor. This simplification captures how real batteries respond to load. When no current flows, the terminal voltage equals the open-circuit voltage supplied by the ideal source. As current increases, the voltage at the terminals decreases linearly according to Ohm's law. The difference between open-circuit and loaded voltage reveals how much potential is lost internally. Because the resistance is typically only a fraction of an ohm, even slight measurement errors or contact resistances can distort results, so careful procedure is required.
The Measurement Formula
The calculator employs the straightforward relationship between voltage drop and current:
In this expression, is the battery's open-circuit voltage measured with no load, is the terminal voltage while supplying current, and is the load current. Subtracting the loaded voltage from the open-circuit value yields the drop across the internal resistor. Dividing by current produces the resistance in ohms. The same approach can be extended to estimate the power lost inside the cell:
Power dissipated internally not only reduces efficiency but also heats the battery. Excess heat accelerates chemical degradation, which further increases resistance, creating a feedback loop that shortens lifespan. For this reason, high-performance applications such as electric vehicles or drones select cells with minimal internal resistance and use battery management systems to monitor temperature rise.
Why Internal Resistance Matters
Consider two identical-looking lithium-ion cells. One might exhibit an internal resistance of only 20 milliohms, while the other, having endured many charge cycles, has climbed to 80 milliohms. If both cells deliver a 5 ampere current, the fresh cell loses internally () whereas the aged cell drops more. That extra drop may push the terminal voltage below the cutoff threshold of a device, causing premature shutdown even though significant capacity remains. In high-drain devices like power tools, small differences in internal resistance can determine whether the tool maintains torque under load or stalls.
Internal resistance also influences charging. During fast charging, the charging source applies current that produces heat according to . Cells with higher resistance heat more for the same current, so manufacturers recommend slower charging rates for aged batteries to avoid thermal runaway. Assessing this parameter helps design safer charging profiles and identify packs that may need replacement before posing risks.
Example Internal Resistances
The table below lists representative open-circuit voltages and internal resistances for several common battery chemistries under a 1 ampere test load. Values vary among manufacturers and depend on temperature and state of charge, but the figures illustrate typical ranges.
| Chemistry | Nominal Voltage (V) | Typical (Ω) |
|---|---|---|
| Alkaline AA | 1.5 | 0.15 |
| NiMH AA | 1.2 | 0.02 |
| Li-ion 18650 | 3.7 | 0.02 |
| Lead-acid (12 V, small) | 12.0 | 0.005 |
| Lead-acid (12 V, aged) | 12.0 | 0.02 |
An alkaline AA cell's relatively high resistance causes significant voltage sag when powering digital cameras or motorized toys that demand amperes of current. Nickel-metal hydride cells handle those loads better due to their low resistance. Lead-acid batteries used in automotive starters begin life with only a few milliohms, allowing hundreds of amperes to crank engines. As they age, resistance climbs, resulting in dim headlights and sluggish starting in cold weather.
Improving Measurement Accuracy
Accurately determining internal resistance requires minimizing external factors. Use thick, short leads to reduce additional resistances, and ensure secure contacts free of corrosion. Measure the open-circuit voltage after the battery has rested for several minutes to allow surface charge to dissipate. For the loaded measurement, apply a known resistor or electronic load that draws substantial current yet remains safely within the battery's discharge limits. A load that is too small will produce a tiny voltage drop that may be swamped by meter error, while an excessively large load may overheat the battery or cause the voltage to collapse near zero, invalidating the calculation. In research settings, four-wire Kelvin connections separate current-carrying and voltage-sensing paths to eliminate lead resistance, but for hobby purposes, careful technique with a digital multimeter usually suffices.
Temperature strongly affects internal resistance: colder batteries exhibit higher resistance because ion mobility decreases. If you test a cell at 0°C and again at 25°C, you may see the value drop by 50% or more. Consequently, when monitoring the health of a battery over time, keep test conditions consistent to avoid misinterpreting temperature effects as degradation. Likewise, state of charge matters. Many batteries show a U-shaped curve where resistance is highest when nearly empty or full and lowest in the middle. Taking readings at a standard state of charge, such as 50%, improves comparability.
Using the Calculator
To operate this tool, gather three pieces of data: the open-circuit voltage after the battery has rested, the voltage while supplying a known current, and the value of that current. Enter these numbers, and the calculator reports internal resistance in ohms along with the power dissipated inside the cell. Because the calculation is linear, you can repeat it with different loads to see if resistance remains consistent. Significant variation may indicate measurement error or a cell behaving nonlinearly due to chemical limitations.
Understanding internal resistance empowers better decisions. For portable electronics, selecting low-resistance cells ensures longer runtimes and stable voltage. In renewable energy systems, monitoring resistance can flag failing battery banks before outages occur. Hobbyists building high-performance flashlights or drones gain insight into why some cells perform better than others. By quantifying this hidden characteristic, the calculator helps translate raw voltage readings into a richer picture of battery health and capability. Though the physics underlying electrochemistry can be complex, this simple resistance model provides an accessible window into the battery's inner workings and offers practical guidance for everyday experiments and sophisticated designs alike.