Phys 4, Section 2 Feb 4, 2002
Current is the motion of
Assume an electric field E is established across a straight piece of
wire of cross-section A. Under the influence of the electric field
charged particles in the (conducting) wire will start drifting through the
field. Assume the average drift velocity of the charges is vd
and the density of charges is n. Then the charge dq moving past a
particular cross-section of the wire is
The drift velocity is surprisingly low. Assume a wire of diameter 1 mm carries a current of 2.0 A. If the density of free electrons in the wire is 8.5 × 1028 electrons per cubic meter, the drift velocity is only about 0.1 mm/s and an electron would require almost 2 hours to travel one meter down the wire.
Resistivity ρ is the ratio of the magnitudes of electric field E and current density J:
ρ = E/J with units (V/m)(A/m2) = (V/A)٠m = Ω٠m where Ω = V/A is an ohm.
If a wire has uniform cross-section A and length L, with resistivity ρ and a voltage V across the ends of the wire, then
E = ρJ V/L = ρI/A V = (ρL/A)I define resistance R = ρL/A
Resistance is the ratio of the potential across a material to the
current through the material.
Although R is generally considered a constant for a particular resistor, R generally varies with temperature, with a proportionality constant α dependent on the material:
dR/dT = αR
Last modified on February 11, 2002