Chapter 27: Current and Resistance
Learning Goals
- Understand electric current both macroscopically and microscopically.
- Know Ohm's law, and how it defines resistance.
- Know how resistance depends upon temperature.
- Understand electrical energy and power.
Electric Current
The electric current flowing in a conducting medium is defined as
where dQ is the flux of current flowing in time dt. The units of
current are Coulomb/sec = Amperes (A).
Conductors have charge carriers (electrons) which drift through
the material with an average drift velocity given by
where n is the number of charge carriers per unit volume, A is
the cross-sectional area of the conductor, and q is the carrier
charge. Since n is typically on the order of Avogadro’s number,
the drift velocity for most situations turns out to be fairly
low - on the order of a mm/sec.
Current Density, Conductivity and Resistivity
Current density is defined as the current per unit area.
It is proportional to the electric field:
where s
is the conductivity of the material. The inverse of
conductivity is resistivity:
Ohm’s Law
Materials whose resistivity is independent of the applied
electric field obey Ohm’s Law:
where R is the resistance of the conductor. Semiconductors are
and important class of materials that do not obey Ohm's Law.
Resistance is
related to resistivity:
where A and L are the area and length of the conductor.
Temperature Dependence
Most materials are characterized by a resistivity that increases
linearly with temperature:
where r
0 is the resistivity at temperature T0, and a
is the temperature coefficient of resistivity.
Power
Power dissipated across any electrical device is equal to
Power Dissipated as Heat by Resistors
Resistors dissipate power as heat, and this heat dissipation
is given by
