Electric current

Charges on the move

Narrated video. Transcript:

So far our charges have sat still. Now let them move. A flash of lightning, the glow of a torch bulb, a signal running along a nerve: in each one, charges are flowing.

Picture a small area held across the flow. Charges cross it, positive ones going forward, negative ones going backward. Each one counts.

Let q plus be the positive charge that crosses forward in a time t, and q minus the negative charge that crosses forward. The net charge that crosses forward is q equals q plus minus q minus.

The current is the rate at which this net charge crosses: I equals q over t. If the current changes with time, we take a very short interval: I of t equals dQ by dt, the limit of ΔQ over Δt.

The SI unit of current is the ampere. One ampere means one coulomb of charge crossing every second.

How many electrons is that? Each carries 1.6 × 10⁻¹⁹ coulomb, so one coulomb is 1 over 1.6 × 10⁻¹⁹, that is 6.25 × 10¹⁸ electrons, crossing every second.

Currents come in very different sizes. A lightning stroke carries tens of thousands of amperes for a moment. Household appliances take about an ampere. The currents in our nerves are only microamperes.

One rule about direction. The current points the way positive charges move. Electrons drifting to the left give a current to the right. This is called the conventional current.

Worked example. A charge of 60 coulomb passes through a heater coil in 2 minutes. 2 minutes is 120 seconds, so I equals 60 over 120, which is 0.5 ampere.

Currents in conductors

Narrated video. Transcript:

Which materials let charges flow? In a metal, the atoms give up some of their outer electrons. The positive ions stay fixed in place, and these free electrons wander through the whole piece of metal.

In an electrolyte, like salt water or the acid in a car battery, both positive and negative ions can move. Their motion makes a current too.

Look closely at a copper wire with no battery. The free electrons are not at rest. They dart about at high speeds, colliding with the ions, in completely random directions.

Now count the electrons crossing a cross-section. Some cross to the right, about the same number cross to the left. The net charge crossing is zero, so there is no current.

Now put a field E along the wire. Electrons are negative, so the force on each one, minus e E, points opposite to E. They are pushed, on the whole, against the field.

Count again. Now more electrons cross one way than the other. There is a net flow of charge, and that is a current. Its direction is along E, opposite to the electrons.

Charge some plates and join them with a wire, and a current flows only for a moment. The charges spread out, the field disappears, and the current stops.

To keep a steady current, something must keep the field alive: keep pushing charges round so the ends of the wire stay at different potentials. That is the job of a cell or a battery.

So we need two things for a steady current: free charge carriers that can move, and a field that is maintained by a source, like a cell.

Try it: count the charge

Interactive simulation. Things to try:

• Watch the dashed cross-section. The counters add up how many electrons cross it each way.
• Set the battery to 0 V and press Reset count. Electrons still cross, but about as many go each way: the net charge, and the current, stay near zero.
• Turn the voltage up again. Now the net count grows steadily, and I = q/t settles to a steady value.
• The electrons cross mostly to the left, but the conventional current arrow points to the right. Reverse the battery and both flip.

Counting electrons

A steady current of 0.5 A flows through a torch bulb for 2 minutes. How many electrons pass through the filament? (e = 1.6 × 10⁻¹⁹ C)

1. 6.25 × 10¹⁸
2. 6.25 × 10¹⁷
3. 3.75 × 10²⁰
4. 6.0 × 10¹

Moving but no current

The free electrons in a copper wire with no battery attached move at about 10⁵ m/s. Why is there no current in the wire?

1. Their speed is too small to make a current
2. The positive ions move the opposite way and cancel them
3. Their directions are random, so as many cross any section one way as the other
4. The electrons are all trapped inside their atoms

Summary

• Current: I = q / t
• Instantaneous current: I(t) = lim ΔQ/Δt = dQ/dt
• One ampere: 1 A = 1 C s⁻¹ (6.25 × 10¹⁸ e per s)

• Electric current is the net charge crossing an area per unit time. Its SI unit is the ampere.
• The direction of current is the direction in which positive charges move; electrons move the opposite way.
• In metals the carriers are free electrons; in electrolytes both positive and negative ions move.
• With no field, free electrons move randomly and there is no net current. A field maintained by a cell gives a steady current.