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Electric Current and Drift Velocity

Electric current is the rate of flow of electric charge through a cross-section of a conductor. Drift velocity is the small average velocity with which free electrons move opposite to the applied electric field inside a conductor.

In one line: Current from many slow drifters: a huge number of electrons moving slowly can still give a large current.

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Understand it

  • When an electric field is applied across a metallic conductor, free electrons do not rush through the wire at very high speed.
  • They undergo frequent collisions with ions and acquire a small average drift velocity.
  • The measurable current depends on the number density of electrons, charge of each electron, area of cross-section, and drift velocity.
  • This microscopic model explains why current starts almost immediately in a circuit even though individual electrons drift slowly.

Example

In a copper wire connected to a cell, electrons drift from the negative terminal side toward the positive terminal side, while conventional current is taken from positive to negative through the external circuit.

Formula and rule

Key formulae: I = dq/dt, where I is current in ampere, dq is charge in coulomb, and dt is time in second; vd = eEτ/m, where e is electronic charge in coulomb, E is electric field in volt per metre, τ is relaxation time in second, and m is electron mass in kilogram; I = neAvd, where n is number density in m−3 and A is area in m2.

Use these for steady current in a metallic conductor under an applied electric field.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A wire has n = 8.0 × 1028 m−3, A = 1.0 × 10−6 m2, and drift velocity vd = 2.0 × 10−4 m s−1.

  1. 1Current I = neAvd = (8.0 × 1028)(1.6 × 10−19)(1.0 × 10−6)(2.0 × 10−4) A = 2.56 A.
  2. 2This means 2.56 C of charge crosses any section of the wire each second.

Method you can reuse

  1. 1Identify the microscopic quantities n, e, A, and vd.
  2. 2Convert area to m2 if needed.
  3. 3Substitute in I = neAvd.
  4. 4For direction questions, remember conventional current follows the electric field in a metal, while electron drift is opposite.

Visual tip

A useful diagram shows a metallic wire connected to a cell, electric field from positive to negative potential, conventional current along the electric field, and electron drift opposite to it. Label A as cross-sectional area and mark vd for electron drift.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why can a wire carry a noticeable current even when the drift velocity of electrons is very small?

Think first, then show answer
A wire can carry a noticeable current because it contains a very large number of free electrons per unit volume. Even a small drift velocity, when multiplied by electron number density, cross-sectional area, and electronic charge, produces measurable current according to I = neAvd.

Common wrong answer

Writing I = nAvd without the electronic charge e gives a dimensionally wrong answer and usually an unrealistically large value.

Don't mix this up

Students often write that electrons move in the same direction as conventional current. In metals, electron drift is opposite to conventional current because electrons carry negative charge.

Exam tip

For derivations, clearly separate electron drift direction from conventional current direction, and write the final current relation as I = neAvd with correct units.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions may ask for the relation between current and drift velocity, the direction of electron drift, a derivation using relaxation time, or a numerical calculation of current, area, or drift speed.
  1. 1

    Enough for 1 mark

    Electric current is the rate of flow of electric charge through a cross-section of a conductor. Drift velocity is the small average velocity with which free electrons move opposite to the applied electric field inside a conductor.

  2. 2

    Add for 2 marks

    Example: In a copper wire connected to a cell, electrons drift from the negative terminal side toward the positive terminal side, while conventional current is taken from positive to negative through the external circuit.

  3. 3

    Add for 3 marks

    When an electric field is applied across a metallic conductor, free electrons do not rush through the wire at very high speed.

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