# NOTES7 - Direct Currents In these notes we consider the...

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11/16/03 Direct Currents In these notes, we consider the motion of charges constituting direct (DC) currents. In contrast to time varying or alternating (AC) currents, DC currents do not vary with time Point Form of Ohm’s Law There are two types of electric currents: convection and conduction currents. Convection currents arise from the transport of charged particles through a vacuum or gas. Examples include moving ions in the ionosphere or electrons in a CRT beam. Conduction currents arise from the drift motion of charges through a medium. In linear media, the conduction current density is proportional to the applied electric field: 2 [A/m ] r σ ρ == E JE where = 1/ r [S/m (Siemens/meter)] is the conductivity and r [ ] is the resistivity of the material . This equation is clearly related to the Ohm’s law of circuit theory; in field theory, it is called the point form of Ohm’s law . A table of resistivities and conductivities of common materials follows. m (Ohm meters) Ω⋅ Table of Material Resistivities and Conductivities Material r [ -m] [S/m=mho/m] Classification Aluminum 2.83 10 -8 × 353 10 7 . × Good conductor Copper 11 0 -8 .69 × 58 7 . × Good conductor Gold 21 0 -8 .44 × 410 7 . × Good conductor Nickel 7.24 10 -8 × 138 7 . × Good conductor Silver 0 -8 .62 × 617 7 . × Good conductor 1

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Germanium 045 . 2 2 0 Semiconductor Silicon 640 156 10 3 . × Semiconductor Seawater 0.25 4.00 Semiconductor Amber 500 14 . × 200 10 15 . × Good Insulator Glass 10 10 10 14 10 10 10 14 −− Good Insulator Petroleum Oil 10 14 10 14 Good Insulator Quartz 750 10 17 . × 130 18 . × Good Insulator In conductors, the conductivity can be factored further into material properties called the electron mobility , µ e , and the free-electron charge density , ρ e : σ ρµ = − ee , the negative sign arising because of the negative charge density of electrons (conductivity is a positive quantitiy). In semiconductors, there are often two species of free charges that may exist: electrons and holes. Holes are atoms which have lost a valence electron, leaving a net positively charged atom. The atom may “fill” the hole by borrowing an electron from a neighboring atom; when the borrowing process proceeds from atom-to- atom in the material, we effectively have a movement of positive charge. For this positive charge movement, a hole mobility h and
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NOTES7 - Direct Currents In these notes we consider the...

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