FIGURE 27.14 shows two identical lightbulbs in the wire connecting two charged capacitor plates. Both bulbs glow as the capacitor is discharged. How do you think the brightness of bulb A compares to that of bulb B? Is one brighter than the other? Or are they equally bright? Think about this before going on.

FIGURE 27.14 How does the brightness of bulb A compare to that of bulb B?

You might have predicted that B is brighter than A because the current $I$, which carries positive charges from plus to minus, reaches B first. In order to be glowing, B must use up some of the current, leaving less for A. Or perhaps you realized that the actual charge carriers are electrons, moving from minus to plus. The conventional current $I$ may be mathematically equivalent, but physically it’s the negative electrons rather than positive charge that actually move. Because the electrons get to A first, you might have predicted that A is brighter than B.

In fact, both bulbs are equally bright. This is an important observation, one that demands an explanation. After all, “something” gets used up to make the bulb glow, so why don’t we observe a decrease in the current? Current is the amount of charge moving through the wire per second. There are only two ways to decrease $I\text{:}$ either decrease the amount of charge, or decrease the charge’s drift speed through the wire. Electrons, the charge carriers, are charged particles. The lightbulb can’t destroy electrons without violating both the law of conservation of mass and the law of conservation of charge. Thus the amount of charge (i.e., the number of electrons) cannot be changed by a lightbulb.

Do charges slow down after passing through the bulb? This is a little trickier, so consider the fluid analogy shown in FIGURE 27.15. Suppose the water flows into one end at a rate of 2.0 kg/s. Is it possible that the water, after turning a paddle wheel, flows out the other end at a rate of only 1.5 kg/s? That is, does turning the paddle wheel cause the water current to decrease?

FIGURE 27.15 A current dissipates energy, but the flow is unchanged.

We can’t destroy water molecules any more than we can destroy electrons, we can’t increase the density of water by pushing the molecules closer together, and there’s nowhere to store extra water inside the pipe. Each drop of water entering the left end pushes a drop out the right end; hence water flows out at exactly the same rate it flows in.

The same is true for electrons in a wire. The rate of electrons leaving a lightbulb (or any other device) is exactly the same as the rate of electrons entering the lightbulb. The current does not change. A lightbulb doesn’t “use up” current, but it does—like the paddlewheel in the fluid analogy—use energy. The kinetic energy of the electrons is dissipated by their collisions with the ions in the metal (atomic-level friction) as the electrons move through the atoms, making the wire hotter until, in the case of the lightbulb filament, it glows. The lightbulb affects the amount of current everywhere in the wire, a process we’ll examine later in the chapter, but the current doesn’t change as it passes through the bulb.

There are many issues that we’ll need to look at before we can say that we understand how currents work, and we’ll take them one at a time. For now, we draw a first important conclusion: Due to conservation of charge, the current must be the same at all points in an individual current-carrying wire.

FIGURE 27.16a summarizes the situation in a single wire. But what about FIGURE 27.16b, where one wire splits into two and two wires merge into one? A point where a wire branches is called a junction. The presence of a junction doesn’t change our basic reasoning. We cannot create or destroy electrons in the wire, and neither can we store them in the junction. The rate at which electrons flow into one or many wires must be exactly balanced by the rate at which they flow out of others. For a junction, the law of conservation of charge requires that

where, as usual, the $\text{Σ}$ symbol means summation.

FIGURE 27.16 The sum of the currents into a junction must equal the sum of the currents leaving the junction.

Full Alternative Text

This basic conservation statement—that the sum of the currents into a junction equals the sum of the currents leaving—is called Kirchhoff’s junction law. The junction law, together with Kirchhoff’s loop law that you met in Chapter 26, will play an important role in circuit analysis in the next chapter.