Electricity and Magnetism Physics 208 Dr. Tatiana Erukhimova Lectures 18-19

Current, Ohm’s Law, Etc.

Resistance does not vary with the applied voltage 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

Problem 4 Two wires having different resistivities ρ1 and ρ2 and equal cross sections, a, are connected end to end. Their lengths are l1 and l2. If a battery is connected to this system such that a potential difference of V is maintained between the ends, What will be the current densities in the wires? What will be the potential difference across each wire? Will there be any charge on the surface where the wires are connected?