The last several chapters have focused on the physics of electric forces, fields, and potentials. Now we’ll put those ideas to use by looking at one of the most important applications of electricity: the controlled motion of charges in electric circuits. This chapter is not about circuit design—you will see that in more advanced courses—but about understanding the fundamental ideas that underlie all circuits.

FIGURE 28.1 shows an electric circuit in which a resistor and a capacitor are connected by wires to a battery. To understand the functioning of this circuit, we do not need to know whether the wires are bent or straight, or whether the battery is to the right or to the left of the resistor. The literal picture of Figure 28.1 provides many irrelevant details. It is customary when describing or analyzing circuits to use a more abstract picture called a circuit diagram. A circuit diagram is a logical picture of what is connected to what.

FIGURE 28.1 An electric circuit.

A circuit diagram also replaces pictures of the circuit elements with symbols. FIGURE 28.2 shows the basic symbols that we will need. The longer line at one end of the battery symbol represents the positive terminal of the battery. Notice that a lightbulb, like a wire or a resistor, has two “ends,” and current passes through the bulb. It is often useful to think of a lightbulb as a resistor that gives off light when a current is present. A lightbulb filament is not a perfectly ohmic material, but the resistance of a glowing incandescent lightbulb remains reasonably constant if you don’t change $\text{Δ}V$ by much.

FIGURE 28.2 A library of basic symbols used for electric circuit drawings.

FIGURE 28.3 is a circuit diagram of the circuit shown in Figure 28.1. Notice how the circuit elements are labeled. The battery’s emf $\epsilon$ is shown beside the battery, and $+$ and $-$ symbols, even though somewhat redundant, are shown beside the terminals. We would use numerical values for $\epsilon$, $R$, and $C$ if we knew them. The wires, which in practice may bend and curve, are shown as straight-line connections between the circuit elements.

FIGURE 28.3 A circuit diagram for the circuit of Figure 28.1.