Electromotive Force (emf)

A conductor is able to sustain a steady current only if it is part of a closed loop: a complete circuit. Otherwise, charge would accumulate at one of the extremes of the circuit for no reason, creating a self-sustained electric field (which we now takes some energy). Therefore, for a current to exist, there must be some part in the circuit where moving charges gain some potential energy, similarly as pump lifts water to the top of a fountain. Such circuit element able to elevate charges to a higher potential is called a source of electromotive force $\mathcal E$ (emf).

We define an ideal source of emf by equating $\mathcal{E}$ and the voltage between its terminals

Remarks

• SI units: measured in volts (V)
• Sources of emf: chemical reactions in batteries, solar cells, electric dynamos…
• The voltage of a battery indicates its emf. Typical values: 1.5V, 5V, 9V…
• An ideal source of emf maintains a constant potential difference between its terminals regardless of the current through it. The external circuit is what fixes the current, although it cannot exceed the maximum current that the battery can deliver.
• Current flows from the positive pole to the negative pole along the circuit, but from negative to positive inside the battery thanks to the emf. In contrast, electrons travel from the negative to the positive pole along the circuit, and from positive to negative inside the battery.

https://youtu.be/w82aSjLuD_8 https://youtu.be/Xe-Csmw9mb8 https://youtu.be/Xe-Csmw9mb8

#Real Batteries

Real batteries present some internal resistance to a current, hence the potential difference across the battery is not exactly the same as the emf, $V_{ab}\leq \mathcal E$.

This effect is normally modeled by an ideal source in series with a resistor $r$