A real cell is not a perfect source. Some of the energy it gives each coulomb is spent inside the cell itself, on its own internal resistance, so the voltage you measure across the terminals drops as soon as current flows.
The electromotive force (e.m.f.) is the energy supplied per unit charge by a source, the total energy each coulomb gains. A real source has internal resistance r, so when a current I flows, some energy is lost inside it: the terminal potential difference is V = E − Ir. The e.m.f. equals the terminal p.d. only when no current flows.
Draw more current from the cell and watch the terminal voltage fall below the e.m.f. by the lost volts Ir. Change the internal resistance and see how a high-r cell sags under load.
Energy is conserved around the whole loop, inside the cell included.
| Relation | Meaning | Unit |
|---|---|---|
| E = energy / charge | electromotive force | volt (V) |
| V = E − Ir | terminal potential difference | volt (V) |
| lost volts = Ir | energy spent inside the source | volt (V) |
Four quick checks tied to this lesson. Each correct answer earns XP and lights this skill on your star map.
The electromotive force of a source is the:
The terminal potential difference of a cell is given by:
A cell of e.m.f. 1.5 V has internal resistance 0.50 Ω and supplies 2.0 A. The lost volts are:
The e.m.f. of a cell equals its terminal potential difference only when:
Internal resistance is where a cell loses energy as heat.
The e.m.f. is not simply the voltage you read across a battery in use; that is the terminal p.d., which is lower by Ir. Use a minus sign: V = E − Ir. The internal resistance is in series with the external circuit, so the same current flows through it, and the cell is warmest when delivering a large current into a small external resistance.
Unlocks once the checks above are done. Worth more XP, written to AS Paper 1 and 2 standard.
A cell of e.m.f. 6.0 V and internal resistance 0.50 Ω drives a current of 2.0 A. The terminal potential difference is:
A battery of e.m.f. 12 V and internal resistance 1.0 Ω is connected to a 5.0 Ω resistor. The current is:
When a graph of terminal p.d. against current is plotted for a cell, the magnitude of the gradient gives the:
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