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Current, charge and the direction problem

Three definitions run the whole of electricity: current as a rate of flow of charge, potential difference as energy per coulomb, and resistance as their ratio. And one historical accident runs alongside them, because the arrows on every circuit diagram point the wrong way.

Year 12AQA 3.5.1.1

IN THIS TOPIC

  • Use I = ΔQ/Δt, with the coulomb as the unit of charge.
  • Use V = W/Q, with the volt as a joule per coulomb.
  • State the definition R = V/I, and keep conventional current and electron flow straight.

WHAT YOU PROBABLY THINK

The current arrows show which way the electrons go.

Current is a rate

Electric current is the rate of flow of charge:

I = ΔQΔtON YOUR DATA SHEET

Stand at one cross-section of a wire and count the charge passing per second: that count is the current. One amp is one coulomb of charge per second, which makes the coulomb an amp second, and rearranging gives the workhorse ΔQ = IΔt.

Current is a rate: the charge crossing a section of the wire every secondcount the charge crossing here each secondone amp = one coulomb per second
FIG. 1Charge carriers drifting through a wire. The current is the charge crossing the marked plane each second.

Charge itself comes in fixed lumps: every electron carries 1.60 × 10−19 C, a constant printed in the data booklet. Any measured charge is a whole number of those lumps, which is how questions convert between coulombs and electron counts.

The direction problem

In the 1750s Benjamin Franklin had to guess which way the invisible moving stuff flowed, and labelled the terminals accordingly. It was a fifty-fifty call, and he lost. The electron was not discovered for another 140 years, by which time every rule, diagram and convention had been built on the wrong guess, so physics kept it.

Conventional current runs from plus to minus; the electrons drift the other way+−conventional currentelectron driftabout a tenth of a millimetre per second
FIG. 2Conventional current runs from the positive terminal to the negative; the electrons drift the opposite way along the same wire.

So conventional current runs from + to − around the outside of a circuit, and that is the direction every arrow and every rule in the subject uses. The electrons, the carriers actually moving in a metal, drift from − to +, backwards. Both statements are true at once; keep the labels attached and nothing goes wrong.

One more indignity for the electrons: they drift at around a tenth of a millimetre per second, slower than a snail. The lights come on instantly because the push travels through the circuit at close to the speed of light. The signal is fast; the particles are not.

Potential difference

Potential difference is the energy ledger of a circuit: the work done per unit charge,

V = WQON YOUR DATA SHEET

so the volt is a joule per coulomb. A 1.5 V cell gives each coulomb 1.5 J on the way through; a component with 1.5 V across it takes 1.5 J back off each coulomb that passes.

Potential difference is energy per coulomb: gained at the cell, delivered at the componenteach coulomb collects V jouleseach coulomb hands over V joulesthe volt is a joule per coulomb
FIG. 3Around the loop, each coulomb collects its energy at the cell and hands it over at the component. Potential difference measures the joules per coulomb at each stage.

Rearranged, W = VQ, and with Q = It, W = VIt: the route from electrical quantities to joules that powers every energy calculation in the unit.

Resistance, defined

Resistance is defined as the ratio of the pd across a component to the current through it:

R = VION YOUR DATA SHEET

measured in ohms, one volt per amp. Notice what this is: a definition, not a law. It says nothing about whether the ratio stays constant as conditions change, and for most components it does not. Which components keep the ratio fixed, and which do not, is the next lesson's entire subject.

THE EXAM BIT

  • ΔQ = IΔt questions hide a unit trap: time must be in seconds. Minutes left unconverted is the classic first-line error.
  • “How many electrons?” means divide the charge by 1.60 × 10−19 C. Expect answers around 1019 to 1021; an answer of a few dozen means the powers went wrong.
  • State directions with their labels: conventional current from + to −, electron flow from − to +. An unlabelled arrow invites the examiner to assume the wrong one.
  • Definitions in words earn marks: current is the rate of flow of charge; pd is the work done per unit charge. Learn them as sentences as well as symbols.
  • Energy from electricity: W = VQ, or W = VIt when the time is given. Choose by what the question supplies.

CHECK YOURSELF

A lamp carries a current of 0.25 A for 2.0 minutes. (a) How much charge passes through it? (b) How many electrons is that?

Show a hint

Seconds first. Then remember that charge comes in fixed lumps.

Show the answer

(a) ΔQ = IΔt = 0.25 × 120 = 30 C.

(b) Each electron carries 1.60 × 10−19 C, so n = 30 / 1.60 × 10−19 = 1.9 × 1020 electrons. A colossal number for a modest lamp, which is why charge behaves as a smooth fluid even though it is grainy.

Current: plus to minus, by convention.

Electrons: the other way, slowly.

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