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Electric Current, Drift Velocity and Ohm's Law
Inside every current-carrying wire, billions of free electrons drift slowly toward the positive terminal, buffeted constantly by collisions with the metal's ions. This lesson connects that microscopic picture — drift velocity — to the macroscopic current you measure with an ammeter, and introduces Ohm's Law, the single most-used relationship in circuit problems.
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Concept Capsule
- Electric current is defined as the rate of flow of charge: I = Q/t (for steady current) or I = dQ/dt (for current that varies with time).
- By convention, current is taken to flow in the direction that POSITIVE charge would move — which is opposite to the actual direction free electrons drift in a metal.
- Free electrons in a conductor don't move in a straight line toward the positive terminal; they undergo constant random collisions with fixed ions, with only a slow net 'drift' superimposed on that chaos.
- Drift velocity v_d is this slow net velocity, typically a fraction of a millimetre per second — remarkably slow compared to how quickly a bulb lights up when a switch is closed (that signal travels near light speed, not at the drift velocity).
- Current relates to drift velocity by I = nAv_d e, where n is the number of free charge carriers per unit volume, A is the conductor's cross-sectional area, and e is the charge of an electron.
- Current density J = I/A is current per unit cross-sectional area, and equals nev_d — useful for comparing current flow across conductors of different thickness.
- Ohm's Law states that for a conductor at constant temperature, the current through it is directly proportional to the voltage across it: V = IR, where R is the resistance (a constant for that conductor at that temperature).
- Materials that obey Ohm's Law (V directly proportional to I) are called ohmic conductors; materials like diodes and semiconductor junctions do NOT obey a simple proportional V-I relationship and are called non-ohmic.
- For an ohmic conductor, a graph of V versus I is a straight line through the origin, and its slope gives the resistance R.
- The SI unit of current is the ampere (A), defined as one coulomb of charge flowing per second (1 A = 1 C/s).
Common KCET Traps
- Confusing the direction of conventional current with the direction electrons actually move — conventional current flows opposite to electron drift.
- Forgetting to convert charge carrier density n or area A into consistent SI units (per m³ and m², not per cm³ and cm²) before substituting into I = nAv_d e.
- Applying Ohm's Law (V = IR) to non-ohmic devices like diodes or bulbs at very different temperatures, where resistance is not constant and V is not simply proportional to I.
- Believing drift velocity is a large, fast quantity — in a typical household wire, drift velocity is only a fraction of a millimetre per second, even though the electrical signal (and the bulb turning on) is nearly instantaneous.
- Inverting the drift velocity formula incorrectly — remember v_d = I/(nAe), with all three of n, A, and e in the denominator.
Drift Velocity and Ohm's Law Circuit Lab
Switch between a microscopic Drift Velocity view (adjust carrier density and wire area to see individual charge carriers drift through a wire) and an Ohm's Law view (adjust resistance and voltage to see the V-I graph and verify the straight-line relationship).