PrayogX › Physics › Current Electricity

Drift velocity of electrons in a wire connected to a battery with internal resistance

A 100 m wire across a 2 V battery with 1 ohm internal resistance: the current appears at once, but each electron drifts at only 0.208 mm/s. R = 1 ohm, I = 1 A, n = 6e28 m^-3, vd = I/(neA) = 0.208 mm/s - option C.

Sub-topics covered

• Resistance from conductivity: R = L/(sigma A)
• EMF and internal resistance: I = eps/(R + r); terminal voltage across the wire
• Free-electron density from density, molar mass and Avogadro's number
• Drift velocity and current: I = n e A vd; J = sigma E = n e vd

What it teaches

• R = 100 / (2e8 x 0.5e-6) = 1 ohm; I = 2/(1 + 1) = 1 A - the wire gets only 1 V of the 2 V
• n = rho NA / M = 6.35e3 x 6e23 / 63.5e-3 = 6e28 m^-3 (one free electron per atom)
• vd = I/(n e A) = 1/4800 m/s = 0.208 mm/s - option C; the field route sigma E/(ne) with E = 0.01 V/m agrees
• The current appears at once because the field is set up through the whole wire; each electron drifts so slowly it would need 5.6 days to travel 100 m
• Traps: ignoring r gives 0.417 mm/s (no option); grams or mm^2 left unconverted give answers off by 1000

Simulation ID

• ADV-2026-P2-PHY-Q01 · revision 2

See this simulation in the library →  ·  open the simulation file on its own