Electronics/Circuit fundamentals

What current measures

After thiswhat you will be able to doCalculate steady current from charge and time, apply charge conservation at a junction, and distinguish conventional current from electron drift.

Questionwhat this lesson answersVoltage tells us energy per charge, but a circuit also needs a rate. What exactly does current measure, and why can the same current be described even though electrons move slowly inside a wire?

Not coveredwhat this lesson leaves outWe define steady current as charge crossing a section per unit time and distinguish conventional direction from electron motion. We do not model the microscopic drift process or alternating current.

Voltage answers an energy question. Current answers a counting question: how much charge crosses one chosen section of the circuit, and how quickly? For a steady current, the definition is

The unit is the ampere, usually shortened to amp:

A current of ${\SI{2}{A}}$ means that ${\SI{2}{C}}$ of charge crosses the section every ${\SI{1}{s}}$. It does not mean that each electron moves at ${\SI{2}{m/s}}$, or that there are ${\SI{2}{C}}$ stored inside each metre of wire. Current is a rate through a boundary, like the number of litres passing a point in a pipe each second.

The section is part of the definition

Imagine drawing an invisible cut across a wire. Count every coulomb that crosses that cut during a time interval and divide by the interval. Move the cut farther along the same unbranched wire: in a steady circuit, the same charge has to cross both cuts, so the current is the same. Charge cannot quietly vanish between them.

Now place the cut at a junction where one path splits into two. Charge conservation says the amount arriving each second must equal the amounts leaving each second:

This is not because current is a fluid that must balance its pressure. It is because charge is not being created or destroyed at the junction. If one branch carries ${\SI{0.7}{A}}$ and another carries ${\SI{0.3}{A}}$, the incoming wire carries ${\SI{1.0}{A}}$ in the steady model.

Which way is the current?

Metals contain mobile electrons, and electrons have negative charge. When an electric field makes them drift, their average motion is opposite to the direction a positive charge would move. By long convention, circuit diagrams call that positive-charge direction the direction of current. This is conventional current.

The convention is not a mistake to correct. It makes the sign of current agree with the sign of charge in the definition. If positive charge moves to the right, the current is to the right. If negative charge moves to the right, the current is to the left. The same convention works for metals, electrolytes, semiconductors, and any circuit in which the mobile carriers are not all electrons.

A wire is not a bucket

When a switch closes, a lamp can respond almost immediately even though any individual electron in the wire may drift only slowly. The electric field that establishes the force travels through the circuit much faster than a particular electron makes its way from the battery to the lamp. The electrons already present throughout the wire begin to drift; the wire does not wait for a new supply of electrons to arrive from the battery.

That observation also separates current from voltage. The field can establish a voltage difference, and the existing mobile charge can respond with a current. The size of that current depends on the path. A thick copper wire and a thin resistive filament can sit in the same circuit while carrying the same series current but producing very different voltage drops.

The next question is therefore not “how much current does a battery contain?” A battery provides a potential difference. A connected component supplies a relationship between that difference and the resulting current. For an ordinary resistor, that relationship is resistance and Ohm’s law.