11.1 Electric Current

Simple circuits used to be part of AP Physics 1. Since 2024–25 they're taught in AP Physics 2, starting here with what current is.

Picture standing at one spot in a wire and counting the charge that crosses the wire's cross section. Current is how much charge passes per second:

$$I = \frac{\Delta q}{\Delta t}$$

The unit is the ampere (A), and 1 A = 1 C/s. Small currents are often given in milliamps (mA = 10⁻³ A).

Charge moves through a circuit because something creates a potential difference across it, such as a battery. The potential difference a battery provides is sometimes called its emf, written ε. It's measured in volts, despite the name “electromotive force.”

Current has a direction along the wire, which is why circuit diagrams use arrows. But it isn't a vector: it doesn't point in a fixed direction in space, it just follows the wire around bends and corners. That's why currents at a junction add as plain numbers, not as vectors.

Conventional current is defined as the direction positive charge would flow: out of the positive terminal of a battery, through the circuit, and back into the negative terminal. In metal wires, the charges that actually move are electrons, which are negative, so they drift the opposite way. Both descriptions give the same effects in circuits, and the AP exam uses conventional current unless it says otherwise.

Even with no current, the free electrons in a metal are zipping around randomly at high speeds. They just move equally in all directions, so no net charge crosses the cross section. Zero current means zero net motion, not motionless electrons.

When a battery is connected, a small drift is added on top of the random motion. That drift is surprisingly slow, often less than a millimeter per second. A light still turns on instantly because the wire is already full of electrons; they all start drifting at almost the same moment, like water in a full hose.

On a graph of charge passed against time, the slope is the current. On a graph of current against time, the area under the curve is the charge that has passed. These graph skills come back with capacitors in 11.8, where the current changes over time.

Current isn't used up as it goes around a circuit. In a single loop, the current is the same at every point: every coulomb that leaves the battery comes back to it. What gets transferred to bulbs and resistors is energy, not charge.