Use the carrier-density current model
Connect drift speed and carrier number density to current using I = Anvq.
Section 9 · Electricity
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 9. Circuit calculations and component sketches are original study practice; full timed assessment, supervised practical competence and human subject-teacher review remain outstanding.
Before you begin
- Use charge, time, energy, power, area and consistent SI units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does n represent in I = Anvq?
What you will learn
- Use I = Anvq for a current-carrying conductor
- Identify cross-sectional area, carrier density, drift speed and carrier charge
- Relate carrier count in a wire segment to charge passing per second
Build the current model from carriers crossing a section
For a conductor of cross-sectional area A, carriers with number density n moving at drift speed v sweep a volume Avt past a section in time t. That volume contains nAvt carriers. If each carrier has charge magnitude q, charge passing is Q = nAvtq.
Divide by t and use I = Q/t to obtain I = Anvq. Here n is in m⁻³, A in m², v in m s⁻¹ and q in C, giving current in amperes. In a metal the mobile carriers are electrons; this expression uses the magnitude of their charge for current magnitude.
Interpret the model rather than memorising symbols
At fixed area and carrier type, a larger drift speed or number density gives a larger current. A thicker conductor can carry the same current with a lower drift speed because more carriers cross the section per second.
Do not confuse drift speed with the much faster propagation of an electrical signal through a circuit. The model describes the average motion of charge carriers in the conductor.
Pause and explain
If A, n and q stay fixed while drift speed doubles, what happens to I?
Worked example
A wire has A = 1.0 × 10⁻⁶ m², n = 8.0 × 10²⁸ m⁻³, drift speed 1.0 × 10⁻⁴ m s⁻¹ and electron charge magnitude 1.6 × 10⁻¹⁹ C. Find current.
Show the worked solution
- Use I = Anvq.
- I = (1.0 × 10⁻⁶)(8.0 × 10²⁸)(1.0 × 10⁻⁴)(1.6 × 10⁻¹⁹).
- Combine powers of ten and state amperes.
Answer I = 1.28 A, approximately 1.3 A.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A conductor has A = 2.0 × 10⁻⁶ m², n = 5.0 × 10²⁸ m⁻³, v = 2.0 × 10⁻⁴ m s⁻¹ and q = 1.6 × 10⁻¹⁹ C. Find current.
Give me a hint
Substitute SI values into I = Anvq.
Compare my reasoning
- I = (2.0 × 10⁻⁶)(5.0 × 10²⁸)(2.0 × 10⁻⁴)(1.6 × 10⁻¹⁹).
- Multiply the numerical factors and add powers of ten.
- State current in amperes.
I = 3.2 A.
Look for these in your work
- All quantities substituted
- Powers handled
- Ampere unit stated
A wire's current is 0.80 A. Let A = 4.0 × 10⁻⁷ m², n = 8.0 × 10²⁸ m⁻³ and q = 1.6 × 10⁻¹⁹ C. Find drift speed.
Give me a hint
Rearrange I = Anvq to make v the subject.
Compare my reasoning
- v = I/(Anq).
- Substitute the stated values with SI units.
- Check the result has unit m s⁻¹.
v = 1.56 × 10⁻⁴ m s⁻¹, approximately 1.6 × 10⁻⁴ m s⁻¹.
Look for these in your work
- Equation rearranged
- Values substituted
- Speed and unit checked
Two wires of the same material carry equal current. Wire B has four times the cross-sectional area of wire A. Compare their electron drift speeds.
Give me a hint
In I = Anvq, hold I, n and q fixed and compare v with 1/A.
Compare my reasoning
- For fixed I, v = I/(Anq).
- Drift speed is inversely proportional to area in this comparison.
- A fourfold area gives one quarter the drift speed.
Wire B's drift speed is one quarter of wire A's, under the stated same-material model.
Look for these in your work
- Fixed quantities identified
- Inverse area relationship used
- Ratio stated
Common mistakes
- Using wire diameter where cross-sectional area is required
- Using electron charge in coulombs with number density in non-SI units
- Confusing drift speed with signal speed
What can you explain now?
What does n represent in I = Anvq?
Compare with the explanation
Number density of charge carriers
It is the number of carriers per unit volume.
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Make it stick
Why can a larger wire carry the same current with a lower carrier drift speed?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.