9.1 Electric current
- Syllabus
- 9702–2028–2029
- Topic
- 9.1
- Level
- AS
Learning objectives
9.1.1An electric current is a flow of charge carriers• understand that an electric current is a flow of charge carriers9.1.2The charge on charge carriers is quantised• understand that the charge on charge carriers is quantised9.1.3Q = It• recall and use Q = It9.1.4Use, for a current-carrying conductor, the expression I = Anvq• use, for a current-carrying conductor, the expression I = Anvq, where n is the number density of charge carriers
Electric current needs moving charge carriers
An electric current is a flow of charge carriers. A particle contributes to current only if it has electric charge and moves so that charge crosses a chosen section; neutral particles such as neutrons cannot carry current.
| Medium | Mobile charge carriers |
|---|---|
| metal | free electrons |
| electrolyte | positive and negative ions |
| ionised gas or particle beam | ions, electrons or other charged particles |
| semiconductor | electrons and holes |
Conventional current is defined in the direction positive charge would move. Positive carriers move with conventional current; negative carriers move in the opposite direction. In a metal wire, electrons drift from the negative terminal towards the positive terminal, opposite to conventional current.
The current magnitude tells how rapidly charge crosses the section: 1 ampere means 1 coulomb per second. A larger number of carriers crossing each second, or a larger charge per carrier, gives a larger current.
Current is not a flow of energy and is not a single electron. Charge carriers drift through the material; energy transfer in the circuit is a related but different process.
Charge is quantised in integer multiples of the elementary charge
Electric charge occurs in discrete amounts q=ne, where n is an integer and e≈1.60×10⁻¹⁹ C.
Use the sign to identify positive or negative carriers and interpret n as a count, not a continuously adjustable fraction.
A charge of −3.2×10⁻¹⁹ C corresponds to two excess electrons.
The quantisation statement does not mean every macroscopic measurement visibly jumps by e; huge carrier counts make charge appear continuous.
Charge transferred by a steady current is Q=It
For constant current, charge transferred in time t is Q=It; for changing current, use the area under an I–t graph.
Use seconds and coulombs, and state whether Q is magnitude or signed charge according to the chosen direction.
A 0.50 A current flowing for 4.0 minutes transfers Q=120 C.
Do not use minutes directly with amperes, and do not assume Q=It for a changing current without integrating or finding graph area.
Count drifting carriers to derive and use I = Anvq
In time t, carriers with average drift speed v travel distance vt. The cylinder that crosses a conductor section of area A has volume Avt, so it contains nAvt carriers. Their total charge magnitude is Q = nAvtq. Dividing by t gives I = Q/t = Anvq.
I=Anvq
| Symbol | Meaning | SI unit |
|---|---|---|
| I | current magnitude | A |
| A | conductor cross-sectional area perpendicular to drift | m² |
| n | number of mobile charge carriers per unit volume | m⁻³ |
| v | average drift speed | m s⁻¹ |
| q | magnitude of charge on each carrier | C |
A wire carries 1.2 A with A = 4.7 × 10⁻⁷ m², n = 8.5 × 10²⁸ m⁻³ and q = 1.60 × 10⁻¹⁹ C. v = I/(Anq) = 1.2/[(4.7 × 10⁻⁷)(8.5 × 10²⁸)(1.60 × 10⁻¹⁹)] = 1.9 × 10⁻⁴ m s⁻¹.
For series sections made of the same material, I, n and q are the same. Therefore v ∝ 1/A: halving wire diameter makes area one quarter as large and drift speed four times larger.
Use cross-sectional area, not diameter: A = πd²/4 for a circular wire. n is a volume number density, not total carriers. Drift speed is usually small and is not the speed at which an electrical signal or energy transfer is established around the circuit.