Library / Electrical / ELE-09
Electrical
Battery internal resistance
Terminal voltage of a battery or cell under load, after the voltage lost across its internal resistance.
- Ref
- ELE-09
- Rev
- v1
- Field
- Electrical
- Result
- V [V]
V is the terminal voltage, E the emf (open-circuit voltage), I the current drawn and r the internal resistance. The calculator takes r in milliohms.
A real battery behaves like a perfect voltage source in series with a small resistor. Draw current and some of the voltage is lost across that internal resistor, so the voltage at the terminals sags below the emf.
Calculator
- Lost volts Ir0.3 V
- Terminal voltage ÷ emf97.62 %
- Power lost inside, I²r6 W
- Short-circuit current E/r840 A
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Terminal voltage falls linearly with the current drawn. A plot of V against I is a straight line with slope −r and intercept E.
- The same current also heats the battery by I²r. Doubling the current quadruples the heat produced inside the cell.
- The most current the battery can give is the short-circuit current E/r. A battery with a small r can deliver very large currents, which is why shorting a battery is dangerous.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (V) | Local step | Change in result |
|---|---|---|---|---|---|---|
| E Emf | 3 to 24 V | 2.7 | 23.7 | 21 | +10% | +10.2 % |
| r Internal resistance | 2 to 200 mΩ | 8.6 | 12.56 | 3.96 | +10% | −0.244 % |
| I Current drawn | 1 to 50 A | 11.85 | 12.58 | 0.735 | +10% | −0.244 % |
Sweep of Current drawn
| Current drawn (A) | Terminal voltage (V) |
|---|---|
| 1 | 12.58 |
| 1.631 | 12.58 |
| 2.659 | 12.56 |
| 4.336 | 12.53 |
| 7.071 | 12.49 |
| 11.53 | 12.43 |
| 18.8 | 12.32 |
| 30.66 | 12.14 |
| 50 | 11.85 |
Sweep one variable
Variables and how each one contributes
Terminal voltage
What the equation gives you. Everything else feeds it.
Emf
Open-circuit voltage of the battery with no current drawn. Shifts the terminal voltage up or down volt for volt.
Current drawn
Current delivered to the load. Lost volts grow in proportion to current, so heavy loads sag more.
Internal resistance
Resistance inside the battery itself. Lost volts grow in proportion to r. Internal resistance typically rises as a battery ages, gets cold or discharges, so the sag gets worse.
Worked example with the values above
- Convert r: 15 mΩ = 0.015 Ω.
- Lost volts: Ir = 20 × 0.015 = 0.3 V.
- Terminal voltage: V = E − Ir = 12.6 − 0.3 = 12.3 V.
Assumptions and limits
- Steady (DC) load current.
- Internal resistance treated as a constant, though it varies with temperature, state of charge and age.
- Linear model: fine for moderate currents, not for fast pulses where chemical effects appear.
Common mistakes
- Mixing milliohms and ohms. 15 mΩ is 0.015 Ω.
- Using the terminal voltage as E. E is the open-circuit voltage.
- Ignoring the sag when sizing a regulator or checking a cut-off voltage.
Statistics and uncertainty
Internal resistance is not a constant. It depends on temperature, state of charge and age. It is usually estimated from two voltage readings at two currents: r = (V1 − V2)/(I2 − I1). Measurement error in V is amplified when the two currents are close together, so the estimate of r then becomes uncertain.
Where it is used
- Predicting voltage sag when a battery drives a heavy load.
- Estimating short-circuit current and internal heating.
- Comparing cells and checking battery health.
Maths you need
- Ohm’s law: the lost volts are Ir
- Emf and terminal voltage: emf is the open-circuit voltage, and the terminal voltage under load is lower