AoNArt of Nanoelectronics
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03 · Introductory

Current as charge flow

Current measures how fast charge crosses a chosen section; it is not the speed of an electron.

75–100 minIntroductory
In this lesson
  • Define DC current as charge transfer per unit time.
  • Use i(t)=dq/dt for time-varying current.
  • Distinguish conventional current direction from electron drift direction.
  • Interpret a current arrow as a reference direction.
Starting question

Does a current of 1 A mean that electrons move through a wire at 1 m/s?

No. Current is a rate of charge transfer, not a carrier velocity. Distinguishing those two ideas is essential before studying circuits, semiconductor transport or electromagnetic propagation.

03.1Average and instantaneous current

Figure 3.1 — Current counts charge crossing a sectionThe arrow defines the positive reference direction of I. A negative result simply means the actual flow is opposite.
II = ΔQ/Δt

If a net charge ΔQ crosses a chosen section during Δt, the average current is

Iavg = ΔQ/Δt

For a time-varying process, instantaneous current is

i(t) = dq(t)/dt

The unit relation is

1 A = 1 C/s

AoN writes constant/DC current with uppercase I and an instantaneous time-varying current with lowercase i(t).

03.2The arrow is a definition, not a prediction

A current arrow defines the positive algebraic direction. If the solution gives I=−3 mA, the physical conventional current has magnitude 3 mA and flows opposite to the arrow.

This is analogous to defining the positive direction on a mechanical axis: a negative velocity is valid motion in the opposite direction, not a failed calculation.

An arrow points left→right and I=−8 mA. State the physical current.
8 mA of conventional current flows right→left.

03.3Conventional current and electron motion

Conventional current direction is defined as the direction positive charge would move. In an ordinary metal the mobile carriers are electrons, so their average drift is opposite to the conventional current direction.

03.4Microscopic bridge: why large current does not require fast drift

For an approximately uniform conductor of cross-sectional area A with carrier number density n, carrier charge magnitude |q| and average drift speed vd, simple carrier counting gives

I = n|q|A vd

This relation is not required for ordinary circuit calculations, but it explains the scale. Using an illustrative copper-like n≈8.5×1028 m−3, A=1.0 mm², |q|=e and I=1 A gives

vd ≈ I/(neA) ≈ 7.3×10−5 m/s ≈ 0.073 mm/s

The exact drift speed depends on material and carrier model; the important point is that a huge number of carriers can produce substantial current with very small average drift velocity.

03.5Two worked charge-transfer examples

Constant current. A steady 2.5 mA flows for 40 ms:

ΔQ = IΔt = 2.5 mA × 40 ms = 100 µC

That is about 6.24×1014 elementary charges in magnitude.

Time-varying current. If i(t)=2t mA for 0≤t≤3 s, then current must be integrated:

ΔQ = ∫03 i(t)dt = ∫032t mA·dt = 9 mC

Integration is simply the inverse operation of i=dq/dt.

03.6Practice for mastery

  1. A constant 4 mA flows for 25 ms. Find the signed transferred charge in the arrow direction.
  2. A solved branch current is I=−0.6 A. Interpret the sign in words.
  3. If q(t)=5t² µC, derive i(t) and evaluate i at t=2 s.
  4. Explain why slow electron drift does not imply a slow response when a switch is closed.
Solutions

1. 100 µC.

2. 0.6 A flows opposite to the chosen reference arrow.

3. i(t)=10t µA, hence i(2 s)=20 µA.

4. Carrier drift and propagation of the electromagnetic disturbance are different physical quantities.

Voltage is energy per charge and current is charge per time. Their product therefore has units and meaning of energy per time: power.

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