Current and Resistance
site menu
Dr. Walter Lewin from MIT
presents Current and Resistance

Electrostatics be damned!!!

The Electric Universe
, by David Bodanis

The amount of flow of charge depends on the material through which the
charges are passing and the potential difference across the materal.
Current is the flow of charge through a given surface per unit time
When charges in a conductor are not in equilibrium

A Classical Conundrum

A given E-field produces a force qE on a charge, and according to Newton's second law the charge will accelerate.

But, if the charges are accelerating why doesn't the current increase with time? Ohm's Law implies that a constant E-field produces a constant current, which suggests a constant velocity. Isn't that a contradiction of Newton's second law?

Every ohmic material has a characteristic resistivity that depends on the properties of the material and on temperature.


The resistance also depends upon the geometry. The resistance is proportional to the length of the material and inversely proportional to its cross-sectional area.

This visualization illustrates a moment from a simulation of epilepsy occurring within the temporal lobe of the brain. The figure shows the electrical current densities throughout the head/brain at one instant of time. Red indicates areas of high electrical current while blue indicates regions of significantly less electrical current. Such visualizations aid researchers in localizing the source of an epileptic seizure.

Current -vs- Voltage

a linear relationship
a non-linear realtionship


"Dr. Cooper realized that it was only the electrons near the top of the Fermi sea that were crucial. “You introduce a small effect,” he said, “and somehow you get a superconductor.”

wikipedia, hyperphysics, simple explanation, chemsoc, princeton

each frame is ten seconds, click to see the whole shebang

Extra Credit Problem (DRS)

Residential building codes typically require the use of 12 gauge copper wire (diameter 0.2053 cm) for wiring receptacles. Such circuits carry currents as large as 20 A. A wire of smaller diameter (with a higher gauge number) could carry this much current, but the wire could rise to a high temperature and cause a fire.
(A) Calculate the rate at which internal energy is produced in 2.10 m of 12 gauge copper wire carrying a current of 20.0 A. (B) Repeat the calculation for an aluminum wire. (C) Would a 12 gauge aluminum wire be as safe as a copper wire?

Quick Quiz 27