What is the relation between drift velocity and electric current?
GradeHunt_TeamGradeHunt Team · · CBSE 12th
Class 12 Current Electricity: how is I = neAvd derived and how does drift velocity depend on electric field and temperature?
drift velocitycurrent electricityclass 12 physics
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Drift velocity (vd) is the small average velocity that free electrons gain in the direction opposite to the electric field in a conductor.
Derivation of I = neAvd:
Take a conductor of cross-section A with n free electrons per unit volume.
- In time t, electrons move a distance vd x t.
- Electrons crossing a section in time t = n x A x vd x t.
- Charge crossing = q = n A vd t e.
- Current I = q / t = n e A vd.
Drift velocity in terms of the field:
Acceleration a = eE/m (opposite to E for electrons).
vd = (eE/m) x tau, where tau is the relaxation time (average time between collisions).
So vd is proportional to E.
Mobility:
Mobility mu = vd / E = e tau / m (SI unit m^2 V^-1 s^-1), so I = neA mu E. Mobility is in the syllabus along with drift velocity, so learn this line too.
How it changes:
1. Electric field or applied voltage: vd increases as E increases (for a given length, E = V/l).
2. Temperature: as temperature rises, collisions become more frequent and tau falls, so for the same field vd falls and the resistance of a metal rises.
3. Area: for a given current, a larger A means a smaller vd (from I = neAvd). But for a fixed potential difference across the wire, vd does not depend on A, because E = V/l.
Order of magnitude: drift velocity is very small (of the order of 10^-4 to 10^-3 m/s, about a millimetre per second or less), yet a bulb lights almost instantly because the electric field travels through the circuit at nearly the speed of light, setting all free electrons drifting at once.
Exam tip: when you write this derivation, draw the conductor with A, vd and the direction of E marked. A labelled diagram makes each step easy to follow.
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