27 Current and Resistance 27-1 Moving Charges and Electric Currents electric currents——that is, charges in motion.

a.A loop of copper in electrostatic equilibrium. b. This movement of charges is a current i.

27-2 Electric Current The current I through the conductor has the Same value at planes aa`,bb`,cc`.

An electric current I in a conductor is defined by: We can fine the charge that passes through the plane in a time interval extending from 0 to t by Integration:

The SI unit for current is the coulomb per Second,also called the ampere(A): 1 ampere=1 A=1 coulomb per second=1C/s

The Direction of Currents A current arrow is drawn in the direction in which positive charge carriers would move, Even if the actual charge carriers are negative and move in the opposite direction.

CHECKPOINT 1 What are the magnitude and direction of the current I in the lower right-hand wire? What are the magnitude and direction of the current I in the lower right-hand wire?

Sample Problem 27-1 charge electrons molecules i= per per per electron molecule second Step one: or

Step two: molecules molecules moles mass volume per = per per unit per unit per second mole mass volume second Step three:

Step four: Step five:

27-3 Current Density

Drift Speed

Sample Problem 27-2 Step one: Step two:

(b) Step one: Step two:

Sample Problem 27-3 atoms atoms moles mass n= per unit = per per unit per unit volume mole mass volume Step one:

Step two: Step three:

Step four:

27-4 Resistance and Resistivity 1 ohm =1Ω ＝ 1 volt per ampere = 1V/A

definition of ρ definition of σ

Calculating Resistance from Resistivity Resistance is a property of an object. Resistivity is a property of a material.

Variation with Temperature

Sample Problem 27-4 Step one: Step two: Step three:

27-5 Ohm ’ s Law Ohm’s law is an assertion that the current through a device is always directly proportional to the potential different applied to the device.

A conducting device obeys Ohm’s law when the resistance of the device is independent of the magnitude and polarity of the applied difference. A conducting material obeys Ohm’s law when the resistivity of the material is independent of the magnitude and direction of the applied electric field.

27-6 A Microscopic View of Ohm ’ s Law

Sample Problem 27-5 Step one:

Step two:

27-7 Power in Electric Circuits

or

Sample Problem 27-6 Step one:

Step two:

27-8 Semiconductors

27-9 Superconductors Superconductors are materials that lose all electrical resistance at low temperatures.