Chapter 27 Current and Resistance Scalar Sense determined by the movement of the positive charge carrier Average Electric Current Instantaneous Electric Current Units:

Microscopic view of current Isn’t E = 0? Current density, j, is the electric current per unit cross sectional area. Current density is a vector. Charge carriers experience a force and accelerate. They collide with the atoms in the metal and are slowed down eventually reaching a terminal velocity called the drift velocity A

Resistance model – Why doesn’t the electron accelerate?

Counting the charge flow A Let:

Current density for electrons A For non-uniform current density E vdvd

Ohm’s Law

Scalar form of Ohm’s Law b a

Units of resistance, resistivity, and conductivity

Temperature effect on resistivity

Superconductors A class of materials and compounds whose resistances fall to virtually zero below a certain temperature, T C –T C is called the critical temperature The graph is the same as a normal metal above T C, but suddenly drops to zero at T C

Superconductor Application An important application of superconductors is a superconducting magnet The magnitude of the magnetic field is about 10 times greater than a normal electromagnet Used in MRI units

Electrical energy and power V The power transformed in an electric device is then: Using Ohm’s Law

Example Problem Given:Copper wire transmission line length = 1500 m diameter = 0.1cm current = 50 A  cu = 1.67 x  -cm Find:Power loss due to heating the wire

Example P27.6 The quantity of charge q (in coulombs) that has passed through a surface of area 2.00 cm 2 varies with time according to the equation q = 4t3 + 5t + 6, where t is in seconds. (a) What is the instantaneous current through the surface at t = 1.00 s? (b) What is the value of the current density?

Example P27.15 A V potential difference is maintained across a 1.50-m length of tungsten wire that has a cross-sectional area of mm 2. What is the current in the wire?

Example P27.29 A certain lightbulb has a tungsten filament with a resistance of 19.0 Ω when cold and 140 Ω when hot. Assume that the resistivity of tungsten varies linearly with temperature even over the large temperature range involved here, and find the temperature of the hot filament. Assume the initial temperature is 20.0°C.

Resistor Values Values of resistors are commonly marked by colored bands

Alternating Current

AC Power ?

Root Mean Square (rms)

Electrical Safety Current kills, not voltage (70 mA) Normal body resistance = 10 5  But could be less than 1000  Take advantage of insulators, remove conductors Work with one hand at a time Shipboard is more dangerous Electrical safety is an officer responsibility