Current, voltage and resistance

A truck battery that sends 720 coulombs through the starter motor in 4 seconds is delivering a current of 180 amperes.

Current is charge per second

Picture standing beside a wire and counting the charge that passes a point. The amount of charge per second is the electric current, I = ΔQ ÷ Δt. Its unit is the ampere (A), named after André-Marie Ampère, and one ampere is one coulomb per second. When a truck engine starts, the battery moves 720 C in 4.00 s: 720 ÷ 4.00 = 180 A. A pocket calculator works on about 0.300 mA, so it takes 1 ÷ 0.000300 ≈ 3,333 seconds, nearly an hour, for a single coulomb to pass through it. Fuses, circuit breakers and many appliances are rated in amperes.

Which way does current go?

In a metal wire the moving charges are electrons, and they travel from the negative terminal of the battery, through the circuit, to the positive terminal. But the direction written on every circuit diagram is the opposite one. Conventional current is defined as the direction positive charge would flow: out of the + terminal and back into the − terminal. This convention goes back to Benjamin Franklin in the 1700s. Both pictures give the same answers for currents and voltages, because negative charge moving left has the same effect as positive charge moving right. In the circuit lab you can show the electrons, the current arrows, or both, and see that they always point opposite ways.

The electrons themselves are slow. Each one bounces off atoms in a zigzag, and its average forward speed, the drift velocity, is tiny. OpenStax works it out for a household copper wire 2.053 mm across carrying 20 A: about 0.45 mm per second, so an electron would need more than half an hour to move one metre. Yet a lamp lights the moment you press the switch. The push travels along the wire almost at the speed of light, because the wire is already full of free electrons; when the ones at one end start to move, the ones everywhere else start too, like water in a full hose.

Voltage: energy for each coulomb

Something has to push the charge around. A battery does work on every coulomb that passes through it, and the energy given to each coulomb is the voltage, measured in volts: 1 V = 1 joule per coulomb. A 1.5 V cell gives every coulomb 1.5 J. A 12 V car battery gives each coulomb 12 J, so moving 5 C through it hands out 60 J. Voltage is always a difference between two points, which is why its other name is potential difference. It rises inside the battery and falls across the bulbs and resistors in the rest of the loop, where the energy turns into light and heat.

A water picture helps. The battery is a pump that lifts water to a height; the voltage is how high it lifts it. The current is how much water flows past each second. A narrow pipe that holds the flow back plays the part of resistance. The picture breaks down if you push it far, but it explains why a bigger voltage drives a bigger current through the same pipe.

Resistance: what holds current back

As free electrons drift, they collide with the atoms of the material and hand over energy, which warms it. This opposition to current is resistance R, measured in ohms (Ω). How much resistance a wire has depends on the material, its length and its thickness: R = ρL ÷ A, where ρ is the resistivity of the material. A longer wire has more resistance; a thicker one has less. The table gives some resistivities from OpenStax. Copper is used for wiring because only silver beats it, and silver costs far more. Nichrome, about 58 times more resistive than copper, is used for the glowing coils in toasters and heaters.

Put numbers in for 10 m of that household copper wire. Its cross-section is π × (1.0265 mm)² ≈ 3.31 × 10⁻⁶ m², so R = 1.72 × 10⁻⁸ × 10 ÷ (3.31 × 10⁻⁶) ≈ 0.052 Ω. That is why we can usually treat connecting wires as having no resistance, as the circuit lab does.