Current, Ohm’s Law, Etc.

where R is resistance Resistance does not vary with the applied voltage resistor

Experimentally it is found that R depends on the material the wire is made of and its dimensions. Does not depend on the shape. In a wire of uniform resistivity and cross sectional area, the electric field is a constant for constant currents.

+ - V

Exercise 1 Given the resistivity of copper, about Ohm-m, what length of 0.5 cm diameter wire will yield a resistance of 10 Ohms?

Current Density Consider current flowing in a homogeneous wire with cross sectional area A.

The Continuity Equation for Steady State Currents Currents and current densities are constant in time – steady state. The flux of out of any closed surface must be zero.

Another form of Ohm’s Law

For steady state situation

Metal: ρ increases with increasing T Resistivity and temperature

Semiconductors: ρ decreases with increasing T

Superconductor Once a current has been established in a superconducting ring, it continues indefinitely without the presence of any driving field Dutch physicist Heike Kamerlingh Onnes - Hg 2003

Water NitrogenOxygen Boils Freezes 100 C (212 F)-196 C (-322 F)-183 C (-297 F) 0 C (32 F) -210 C (-346 F) -223 C (-369 F) Our air is ¾ Nitrogen and ¼ Oxygen

1908- liquefied helium produced First discovered in mercury by Kamerlingh-Onnes in Critical temperature 4.21K. Nobel Prize in Superconductivity

High-T c Superconductivity Liquid nitrogen temperature 77 K Complex ceramic materials were discovered in They exhibit superconductivity at much higher temperatures – above LN temperature! Muller and Bednortz, Nobel Prize 1987

Meissner effect and magnetic levitation