How Does a Cell’s Internal Resistance Vary With Temperature?

A cell’s internal resistance is often lower when the cell is warm and higher when it is cold. This is especially noticeable in electrochemical cells: low temperatures can make a cell deliver less current and cause a larger voltage drop under load.

The trend is common, but not universal in every detail. Internal resistance is an effective description of several processes inside a cell, and those processes respond differently to temperature and operating conditions.

Why warming often lowers internal resistance

A cell’s electrolyte contains mobile ions that carry charge between its electrodes. As temperature rises, ions generally move more readily and the electrolyte’s ionic conductivity increases. A more conductive electrolyte offers less resistance to ionic current.

Temperature can also speed up electrochemical reactions at the electrode surfaces and improve the rate at which reactants move through the cell. These changes reduce some of the voltage losses that appear when current flows. In the simple school-level model, the result is usually stated as: higher temperature means lower internal resistance.

Cooling tends to have the opposite effect. At low temperatures, ion movement and electrode reactions slow down. The cell’s voltage may sag more under load, and its usable power can be reduced. The effect can be substantial in some rechargeable cells, including lithium-ion cells, but the exact size depends on the design and conditions.

What “internal resistance” means

A cell is often modeled as an ideal electromotive force (emf) $E$ in series with an internal resistance $r$. When the cell supplies current $I$, its terminal voltage $V$ is approximately

$$V = E - Ir.$$

If $E$ and $V$ are measured under the same conditions, this model gives

$$r = \frac{E - V}{I}.$$

This $r$ is an effective, or apparent, internal resistance. A real cell does not contain just one ordinary resistor. Its measured voltage loss can include resistance in the electrolyte and electrodes, contact resistance, reaction losses, and concentration changes near the electrodes. Some of these effects depend on how quickly you measure after applying a current.

As a result, a quoted internal resistance is meaningful only alongside conditions such as temperature, state of charge, current, and measurement method. An alternating-current impedance measurement and a short direct-current load test, for example, need not give the same value.

Worked example: comparing two temperatures

Suppose a cell has an open-circuit voltage of $1.50\,\text{V}$. At a particular temperature, a test current of $0.50\,\text{A}$ produces a terminal voltage of $1.30\,\text{V}$. Using the simple model,

$$r = \frac{1.50 - 1.30}{0.50} = 0.40\,\Omega.$$

Now suppose the same cell, at the same state of charge, is tested at a warmer temperature and its terminal voltage under the same current is $1.40\,\text{V}$. For this illustration, assume its open-circuit voltage is still $1.50\,\text{V}$ at the warmer temperature. The apparent resistance is then

$$r = \frac{1.50 - 1.40}{0.50} = 0.20\,\Omega.$$

In this example, the warmer cell has half the apparent internal resistance. The calculation illustrates the usual trend; it does not establish a universal temperature law. A real comparison should use the cell’s open-circuit voltage at each temperature, since that voltage itself may also change with temperature.

Why the trend is not a complete rule

The cell’s total response combines several effects, and temperature does not affect them all in the same way. The relationship may be nonlinear, and it can vary with state of charge, cell age, construction, and the duration and size of the current pulse. In some temperature ranges, different contributions can partly offset one another.

Also, a lower resistance at higher temperature should not be taken as advice to heat a battery. High temperature can accelerate chemical ageing and, for some rechargeable cells, create serious safety risks. Battery operating limits come from the manufacturer, not from the resistance trend alone.

Common mistakes

• Treating the trend as a universal formula. “Resistance falls when temperature rises” is a useful generalization for many cells, not a guarantee of a straight-line relationship for every chemistry or temperature range.
• Confusing internal resistance with the cell’s emf. The emf is not the internal resistance. Temperature can affect both, so a voltage change alone does not identify which quantity changed.
• Comparing measurements made under different conditions. State of charge, current, rest time, and measurement method all matter. Keep them consistent when you compare temperatures.
• Assuming a real cell is a fixed resistor. The simple model is useful for estimating voltage drop, but a cell’s effective resistance can depend on the timescale of the test.

To compare cells fairly, bring each to a known temperature, use the same state of charge and test procedure, and report how the resistance was measured. For the simple load-test model, measure the cell’s open-circuit voltage and its terminal voltage under a known current, then calculate $r=(E-V)/I$.