What is electromotive force (emf) and how can the emf of a battery be measured?

The electromotive force is the work done by a battery on the charge carriers to transport them across the entire circuit, per unit charge. It can be thought of as the specific energy given to the charge carriers.

To measure the emf of a battery, one can connect it in a circuit with a resistor, a voltmeter and an ampere meter. The emf will be the sum of the voltage differences across the resistor and the battery itself: E = U_ext + U_int. Since U_int = Ir, where r is the internal resistance of the circuit, the equation can be rearranged as U_ext = E - Ir. Hence, by measuring U_ext (with the voltmeter) and I (with the ammeter) for multiple values of the external resistor we can plot a graph of U vs I where the emf (E) is the y-intercept.