Our study of current has focused on the discharge of a capacitor because we can understand where all the charges are and how they move. By contrast, we can’t easily see what’s happening to the charges inside a battery. Nonetheless, current in most “real” circuits is driven by a battery rather than by a capacitor. Just like the wire discharging a capacitor, a wire connecting two battery terminals deflects a compass needle, gets warm, and makes a lightbulb glow brightly. These indicators tell us that charges flow through the wire from one terminal to the other.

The one major difference between a capacitor and a battery is the duration of the current. The current discharging a capacitor is transient, ceasing as soon as the excess charge on the capacitor plates is removed. In contrast, the current supplied by a battery is sustained.

We can use the charge escalator model of a battery to understand why. FIGURE 27.19 shows the charge escalator creating a potential difference $\text{Δ}{V}_{\text{bat}}$ by lifting positive charge from the negative terminal to the positive terminal. Once at the positive terminal, positive charges can move through the wire as current I. In essence, the charges are “falling downhill” through the wire, losing the energy they gained on the escalator. This energy transfer to the wire warms the wire.

FIGURE 27.19 A battery’s charge escalator causes a sustained current in a wire.

Eventually the charges find themselves back at the negative terminal of the battery, where they can ride the escalator back up and repeat the journey. A battery, unlike a charged capacitor, has an internal source of energy (the chemical reactions) that keeps the charge escalator running. It is the charge escalator that sustains the current in the wire by providing a continually renewed supply of charge at the battery terminals.

An important consequence of the charge escalator model, one you learned in the previous chapter, is that a battery is a source of potential difference. It is true that charges flow through a wire connecting the battery terminals, but current is a consequence of the battery’s potential difference. The battery’s emf is the cause; current, heat, light, sound, and so on are all effects that happen when the battery is used in certain ways.

Distinguishing cause and effect will be vitally important for understanding how a battery functions in a circuit. The reasoning is as follows:

1. A battery is a source of potential difference $\text{Δ}{V}_{\text{bat}}$. An ideal battery has $\text{Δ}{V}_{\text{bat}}=\epsilon$.

2. The battery creates a potential difference $\text{Δ}{V}_{\text{wire}}=\text{Δ}{V}_{\text{bat}}$ between the ends of a wire.

3. The potential difference $\text{Δ}{V}_{\text{wire}}$ causes an electric field $E=\text{Δ}{V}_{\text{wire}}\text{/}L$ in the wire.

4. The electric field establishes a current $I=JA=\sigma AE$ in the wire.

5. The magnitude of the current is determined jointly by the battery and the wire’s resistance $R$ to be $I=\text{Δ}{V}_{\text{wire}}\text{/}R$.