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Phys 4, Section
2
Feb 4, 2002
Current
Current is the motion of
charge: I
= dq/dt
where I is measured in amperes (A). The direction of the current is always the
direction of positive charge motion. This means that electron flow is always
opposite to the direction of current flow.
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
dq = q(nAvddt)
= nqvdAdt
and the current I is given by
I = dq/dt =
nqvdA.
The current density (J) is defined as J = I/A = n|q|vd.
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.
Resistance
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
Ohm's Law
Resistance is the ratio of the potential across a material to the
current through the material.
R =
V/I
(Ohm's Law)
R is called the resistance of a particular object measured between two
points. Resistivity ρ is a
characteristic of a material, while resistance R is a characteristic of a
specific sample of that material, with size and geometry figured in.
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
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