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Learn7408Paper 1 · Paper 1ElectricityElectric current
Electricity · Subtopic 1 of 6

Electric Current

Current is the rate of flow of charge, I=ΔQΔtI=\dfrac{\Delta Q}{\Delta t}. Charge comes in whole multiples of the elementary charge e=1.60×10−19e=1.60\times10^{-19} C. In a conductor, current depends on the number density of charge carriers, their charge and their drift velocity: I=AnvqI=Anvq. Electrons drift slowly, but the signal travels almost instantly.

Cambridge 9702 Paper 1Cambridge 9702 Paper 2Edexcel YPH11 WPH12AQA 7408 Paper 1≈ 30 minRevision 5 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Use Q=ItQ=It, including the area under a current–time graph.
  • Explain that charge is quantised in multiples of ee.
  • Use I=AnvqI=Anvq to find drift velocity.
  • Explain how drift velocity changes along a non-uniform wire.
Pause and think

Electrons in a copper wire drift at less than a millimetre per second. So why does a light come on the instant you flick the switch, several metres away?

Section 2 of 14

Core idea

Start hereElectrons move at a snail's pace

Flip a switch and the lamp lights instantly, yet the electrons in the wire drift at less than a millimetre per second. The signal travels fast; the charge carriers don't. A simple formula explains both.

The big idea

I=ΔQΔtI=\frac{\Delta Q}{\Delta t}; I=nAvqI=nAvq. Charge is quantised in e=1.60×10−19e=1.60\times10^{-19} C.

1. Deriving I = nAvq

Electrons drifting through a wire
conventional currentelectron drift●●●●●●●●●●●●●●
Electrons drift slowly (millimetres per second) towards the positive terminal, opposite to conventional current.
I=nAvqI=nAvq
  1. length moved in t: vt\text{length moved in }t:\ vt
    Drift speed vv.
  2. N=nAvtN=nAvt
    Carriers in volume AvtAvt.
  3. Q=nAvtqQ=nAvtq
    Each carries qq.
  4. I=Qt=nAvqI=\frac Qt=nAvq
    Divide by tt.
I=nAvqI=nAvq
where
nn
carriers per m³.
AA
cross-section (m²).
vv
drift speed.
qq
charge per carrier.
Worked exampleDrift in copper

n=8.5×1028n=8.5\times10^{28} m−3^{-3}, A=1.0A=1.0 mm², I=2.0I=2.0 A.

Goal
vv.
Strategy
Rearrange; mm² → m².
  1. v=InAqv=\frac I{nAq}
    Rearrange.
  2. =28.5×1028×10−6×1.6×10−19=1.5×10−4 m s−1=\frac{2}{8.5\times10^{28}\times10^{-6}\times1.6\times10^{-19}}=1.5\times10^{-4}\text{ m s}^{-1}
    Evaluate.
Answer0.150.15 mm s−1^{-1}.
✓ CheckTiny, as the hook said ✓.
Worked exampleElectrons per second

0.5 A.

Goal
Number per second.
Strategy
Charge ÷ ee.
  1. 0.5 C per second0.5\text{ C per second}
    Definition.
  2. 0.51.6×10−19=3.1×1018\frac{0.5}{1.6\times10^{-19}}=3.1\times10^{18}
    Divide.
Answer3.1×10183.1\times10^{18} s−1^{-1}.
✓ CheckHuge numbers, tiny charges ✓.
Common misconceptionmm² to m² 11 mm² =10−6=10^{-6} m².
Pause and think

Semiconductor (small nn), same II and AA: drift speed?

Summary

  • I=Q/tI=Q/t; I=nAvqI=nAvq.
  • Charge quantised.
Key words
Drift velocity
Average speed of charge carriers.
HistoryThomson weighs the electron. In 18971897 J. J. Thomson deflected "cathode rays" with electric and magnetic fields and showed they were tiny negatively charged particles, far lighter than any atom. The electron was the first subatomic particle discovered. Millikan measured its charge in 19091909.
Fun factLightning's current. A lightning stroke carries about 30 00030\,000 A, but only for around 3030 microseconds. That's a total charge of just about 11 C, roughly what a phone charger delivers in a few seconds.
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