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Cell EMF, Terminal Voltage & Internal Resistance

Relate a cell’s ideal EMF, internal resistance and a positive resistive load during discharge.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A 12 V ideal EMF supplying 2 A through a 5 Ω load has terminal voltage 10 V and modeled internal resistance 1 Ω.

Terminal voltage = EMF − Ir = IR; internal resistance = EMF/I − load resistance

Worked example

Enter these known values and leave the other values blank.

Ideal source EMF
12 V
External resistive load
5 Ω
Discharge current
2 A
Modeled internal resistance
1 Ω
Loaded terminal voltage
10 V

Assumptions and limitations

  • The model is a constant ideal voltage source in series with a nonnegative resistance and a positive resistive load.
  • EMF, load, current and terminal voltage must be positive. Charging, open-circuit and short-circuit boundary models are not included.
  • Actual batteries depend on state of charge, temperature, current history and chemistry. The inferred resistance describes the supplied operating point, not a universal cell property.

Common questions

Why is loaded terminal voltage below EMF?

In this model, current produces an internal voltage drop Ir. Subtracting that drop gives the voltage available to the external load.

Can internal resistance be zero?

Yes. Zero internal resistance is the ideal-source limit, where loaded terminal voltage equals EMF.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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