Meaning and mechanism
A battery can be approximated by an ideal EMF E in series with internal resistance r. When an external resistor is connected, the same current flows through the internal and external resistances.
When a smaller load resistance increases the current, the internal voltage drop Ir also increases. A battery’s no-load voltage may therefore differ from its operating voltage.
Relationships and conditions
I=E/(R+r), the terminal voltage is V=E−Ir. If V is plotted on the vertical axis and I on the horizontal axis, the intercept is E, and the slope is −r.
Actual EMF and internal resistance can vary with state of charge, temperature, current, and time. A constant-r model is an approximation for limited conditions.
What to observe in the simulation
The slope of V versus I is −r; the intercept is the EMF.
EMF and internal resistance are constant. Chemical reactions and battery life are omitted. Experiment on screen; do not reproduce this with real power supplies, outlets or high voltage.
Key relationships and symbols
I = E/(R+r) · V = E−Ir · P = I²R
| Symbol | Meaning | Unit |
|---|---|---|
| E | Induced EMF | V |
| r | Internal resistance | Ω |
| V | Terminal voltage | V |
Worked example
What is the internal resistance if this battery's V–I slope is −1 V/A?
1 Ω
Common misconceptions
- It is not possible to interpret a decrease in terminal voltage when a large current is supplied as always having the same value as the inherent electromotive force.