EMF and internal resistance

Intermediate

Terminal voltage drops under load.

Key relationV = ε − Ir

A real source has EMF ε and internal resistance r, so terminal voltage V = ε − Ir drops under load. EMF is the open-circuit voltage.

Worked example

A 12 V battery with r = 0.1 Ω delivering 30 A: V = 9 V.

Common mistake

Short circuit current is ε/r.

In more detail

A real cell has an electromotive force (EMF) and an internal resistance. Its terminal voltage falls as current is drawn, V = ε − Ir.

Car batteries have low internal resistance so they can supply high currents to the starter.
Battery testers measure internal resistance to check health.
A battery's voltage drops when a heavy load is connected, because the internal resistance uses up part of the emf.

What is EMF?

The energy per unit charge supplied by the cell, measured in volts, though it is not a force.

Why does voltage drop when current is high?

Because some voltage is used across the internal resistance.

What is the emf of a cell?

The voltage the cell provides when no current is drawn, which is the energy given to each coulomb of charge.