We have developed the idea of a current as the motion of electrons through metals. But the properties of currents were known and used for a century before the discovery that electrons are the charge carriers in metals. We need to connect our ideas about the electron current to the conventional definition of current.

Because the coulomb is the unit of charge, and because currents are charges in motion, it seemed quite natural in the 19th century to define current as the rate, in coulombs per second, at which charge moves through a wire. If $Q$ is the total amount of charge that has moved past a point in the wire, we define the current $I$ in the wire to be the rate of charge flow:

For a steady current, which will be our primary focus, the amount of charge delivered by current $I$ during the time interval $\text{Δ}t$ is

The SI unit for current is the coulomb per second, which is called the ampere A:

The current unit is named after the French scientist André Marie Ampère, who made major contributions to the study of electricity and magnetism in the early 19th century. The amp is an informal abbreviation of ampere. Household currents are typically $\approx 1\text{A}$. For example, the current through a 1200 W hair dryer is 10 A, meaning that 10 C of charge flow through the bulb every second. Currents in consumer electronics, such as stereos and computers, are much less. They are typically measured in milliamps $(1\text{mA}={10}^{-3}\text{A})$ or microamps $(1\mu \text{A}={10}^{-6}\text{A})$.

Equation 27.10 is closely related to Equation 27.1, which said that the number of electrons delivered during a time interval $\text{Δ}t$ is $N_{\text{e}}=i_{\text{e}}\text{Δ}t$. Each electron has charge of magnitude $e\text{;}$ hence the total charge of $N_{\text{e}}$ electrons is $Q=e{N}_{\text{e}}$. Consequently, the conventional current $I$ and the electron current $i_{\text{e}}$ are related by

Because electrons are the charge carriers, the rate at which charge moves is $e$ times the rate at which the electrons move.

In one sense, the current $I$ and the electron current $i_{\text{e}}$ differ by only a scale factor. The electron current $i_{\text{e}}$, the rate at which electrons move through a wire, is more fundamental because it looks directly at the charge carriers. The current $I$, the rate at which the charge of the electrons moves through the wire, is more practical because we can measure charge more easily than we can count electrons.

Despite the close connection between $i_{\text{e}}$ and $I$, there’s one extremely important distinction. Because currents were known and studied before it was known what the charge carriers are, the direction of current is defined to be the direction in which positive charges seem to move. Thus the direction of the current $I$ is the same as that of the internal electric field $\vec{E}$. But because the charge carriers turned out to be negative, at least for a metal, the direction of the current $I$ in a metal is opposite the direction of motion of the electrons.

The situation shown in FIGURE 27.13 may seem disturbing, but it makes no real difference. A capacitor is discharged regardless of whether positive charges move toward the negative plate or negative charges move toward the positive plate. The primary application of current is the analysis of circuits, and in a circuit—a macroscopic device—we simply can’t tell what is moving through the wires. All of our calculations will be correct and all of our circuits will work perfectly well if we choose to think of current as the flow of positive charge. The distinction is important only at the microscopic level.

FIGURE 27.13 The current $I$ is opposite the direction of motion of the electrons in a metal.