Applied Electromagnetics Using Quickfield & MATLAB

Chapter 13: Electrical Circuits

13.1 ELECTRICAL CURRENT AND OHM's LAW

Electrical current I is defined as the total charge that flows through a conductor per unit time or

(13.1)

The SI unit of current is the Ampere ( A) defined as a Coulomb ( C) per second. Benjamin Franklin first adopted the convention that current flows in the direction of positive charge. The motion of negative charge to the left is equivalent to a positive current flow to the right. The charge carriers in a circuit are usually negatively charged electrons, hence the direction of current is taken as opposite to the direction of electron flow. Current flows in proportion to the potential drop V across a conductor and in inverse proportion to the materials resistance R according to Ohm's law

(13.2)

Electrical resistance results from the scattering of electrons by the crystal lattice, phonons, and impurities in a conductor. The unit of resistance is the Ohm ( ?) defined as a volt per Ampere. Experimentally Ohm found that resistance is proportional to the length L and inversely proportional to the cross-sectional area S of a conductor

(13.3)

The resistivity ? is a material property that is geometry independent with S.I. units of ? m. Most metals are good conductors of electricity. Resistivity decreases with lower temperature and becomes identically zero below a transition temperature T c in superconductors. In poorly conducting nonmetals, or insulators, electrons are strongly bound to positive nuclear...

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