Electric current

Switch on a torch and something invisible races through the copper wire faster than you can blink, yet the electrons themselves barely crawl. That "something" is electric current — the directed flow of electric charge that lights the bulb, and it is the starting idea of the whole "Current Electricity" chapter. Inside every metal wire sit countless free electrons, wandering randomly until a cell gives them a push in one direction. This article builds the idea of current from the ground up: what charge is, why it is quantised, how a circuit must be closed for current to flow, why the textbook direction of current is the opposite of how electrons actually move, and — new at this level — how to turn "current" into a number using $I = Q/t$ .

The core insight

Electric current is the rate of flow of electric charge through a conductor, $I = Q/t$ , driven by a cell that makes free electrons drift in one net direction along a closed circuit.

The core idea

Free electrons make metals conduct. Every atom in a metal has outer electrons that are only loosely bound to the nucleus, so they can move freely through the material. With no cell connected, these free electrons dash about randomly in every direction — there is no net flow of charge, even though the electrons are never actually still.

A cell creates directed flow. Connect a cell across the ends of a wire and it sets up a push that makes free electrons drift together in one direction. This net, directed flow of charge is electric current. The drift is slow — individual electrons zig-zag through collisions with atoms — but the push itself is transmitted through the wire almost instantly, which is why the bulb lights up the moment the switch closes.

Charge is measured in coulombs and is quantised. The SI unit of electric charge is the coulomb (C). Charge never appears in an arbitrarily small amount; it always comes in whole-number multiples of the charge on one electron, $e = 1.6\times10^{-19}\ \text{C}$ . So any charge you measure, however large, is really a huge but whole number of electron-charges added together.

Current has a size as well as a direction. More charge crossing a point in the circuit every second means a bigger current — this is the quantitative idea the derivation below turns into a formula. A circuit must be closed — an unbroken path from the cell, through the wire and bulb, and back to the cell — for current to flow at all; if the path is broken anywhere, such as at an open switch, the circuit is open and no current flows, even though the metal still contains plenty of free electrons sitting idle.

Conventional current runs opposite to electron flow. Long before electrons were discovered, scientists defined conventional current as flowing from the positive terminal of a cell, through the external circuit, to the negative terminal. The actual charge carriers in a metal are negatively charged electrons, and they drift the other way — from the negative terminal to the positive terminal. Both descriptions are used side by side: circuit diagrams always follow conventional current, while the physical picture of "what moves" is electron flow.

Figure

A simple torch circuit with a cell bulb and switch showing conventional current arrows from positive to negative around the outside and electron flow arrows the opposite way inside the wire

Instruments and the closed-circuit rule

Current is detected using a galvanometer for small currents, or measured directly using an ammeter, both connected in the path of the circuit. At this stage you only need to know what these instruments are for — detecting and measuring current — not how they work internally. Remember also that "no current flowing" is not the same as "no charge in the wire": an open circuit still has plenty of free electrons sitting inside the metal, they are simply not drifting in any net direction.

Derivation ADefining electric current as charge per unit time

Turn the qualitative idea "more charge flowing per second means a bigger current" into a precise, testable definition that lets you calculate a current from a measured charge and a measured time, and that also fixes the size of the ampere, the SI unit you will use for every circuit problem from here onward.

Step 1. Start from the physical picture: charge $Q$ crosses any fixed cross-section of the wire as current flows, and this happens over some time interval $t$ .

Step 2. Current is defined as the rate at which this charge crosses that point — charge divided by the time taken:

I = \dfrac{Q}{t}

where: $I$ is the electric current (amperes, A), $Q$ is the charge that has flowed (coulombs, C), and $t$ is the time taken (seconds, s).

Step 3. This definition fixes the SI unit of current, the ampere (A), directly from the units of charge and time: a current of one ampere is exactly one coulomb of charge flowing past a point every second, $1\ \text{A} = 1\ \text{C/s}$ .

Step 4. Because charge is quantised in units of $e = 1.6\times10^{-19}\ \text{C}$ , any current, however large it seems, is really a very large but whole number of individual electron-charges drifting past the same point every second — the formula $I = Q/t$ just packages that count into one convenient number.

Worked example

Question: A charge of $12\ \text{C}$ flows through a bulb filament in $4$ seconds when a circuit is switched on. Find (a) the current in the circuit, and (b) the number of electrons that cross the filament in that time.

Step 1. Identify the known quantities: $Q = 12\ \text{C}$ , $t = 4\ \text{s}$ , and the charge on one electron $e = 1.6\times10^{-19}\ \text{C}$ .

Step 2. Apply the definition of current, $I = Q/t$ , to find the size of the current: $I = 12 / 4 = 3\ \text{A}$ .

Step 3. To find the number of electrons $n$ , use the fact that the total charge is $n$ times the charge on one electron, so $n = Q/e = 12 / (1.6\times10^{-19})$ .

Step 4. Carry out the division: $n = 7.5\times10^{19}$ electrons.

Answer: the current is 3 A, carried by about $7.5\times10^{19}$ electrons crossing the filament in those 4 seconds.

Competitive stretch

If the same bulb is left on for $1$ minute ( $60\ \text{s}$ ) instead of $4\ \text{s}$ , and the current stays steady at $3\ \text{A}$ , rearranging $I = Q/t$ gives $Q = I t = 3 \times 60 = 180\ \text{C}$ of charge delivered — a reminder that $I = Q/t$ works both ways, to find current from charge and time, or to find charge from current and time.

Common traps

Writing conventional current and electron flow as moving in the same direction — in a metal they are opposite, even though both describe the same current.
Treating "no current" as "no charge in the wire" — an open circuit still has free electrons present, just not drifting together.
Forgetting that $I = Q/t$ needs $Q$ in coulombs and $t$ in seconds before the answer comes out in amperes — mixing minutes and seconds is a common slip.
Assuming a bigger current means more electrons exist in the wire — a bigger current means more charge crosses a point per second, not more electrons stored in the metal.

Ask the tutor: Want to work through how this same charge-and-time idea connects to potential difference and Ohm's Law in the next topic?

Why does the bulb light up almost instantly if electrons drift so slowly

The electrons themselves move quite slowly through the wire, bumping into atoms as they go. But the electric push from the cell is set up throughout the whole wire almost the instant the switch closes, so every free electron everywhere in the circuit starts drifting together at nearly the same moment — you do not have to wait for one electron to travel all the way from the cell to the bulb.

If conventional current is the wrong direction, why do we still use it

Conventional current was defined before anyone knew electrons carried the actual charge in a metal, and it has stayed the standard ever since because circuit diagrams, formulas, and instruments like ammeters are all built around it consistently. Switching to electron-flow direction now would not change any physics or any answer — it would just relabel an arrow, so the convention was kept.

Does I = Q/t mean current is the same thing as charge

No — charge $Q$ is the quantity being transported, measured in coulombs, while current $I$ is the rate at which that charge is transported, measured in coulombs per second, or amperes. The same charge can correspond to a large current delivered quickly or a small current delivered slowly, depending on the time $t$ it is spread over.