Current � and � Resistance Electric Current Resistance and Ohm’s Law A Model for Electrical Conduction Resistance and Temperature Superconductor Electrical Energy and Power

Electric Current Suppose that the charges are moving per pendicular to a surface of area A The current is the rate at which charge flows through this surface The average current The Instantaneous current is The SI unit of current is the ampere (A):

Electric Current (2) It is conventional to assign to the current the same direction as the flow of positive charge In electrical conductors, the direction of the current is opposite the direction of flow of electrons It is common to refer to a moving charge (positive or negative) as a mobile charge carrier

Microscopic Model of Current We can relate current to the motion of the charge carriers by describing a microscopic model of conduction in a metal The volume of a section of the conduct or of length is If n represents the number of mobile charge carriers per unit volume, the number of carriers in the gray section is If the charge of each carrier is q, total charge in the section is

Microscopic Model of Current (2) If the carrier moves with the speed, the distance during is, thus The average current in the conductor is The speed of the charge carriers v d is an average speed called the drift speed

RESISTANCE AND OHM’S LAW We know that average current is The current density J In some materials, the current density is pr oportional to the electric field: The constant is called conductivity. It is well-known as ohm’s law Materials that obey Ohm’s law is said to be ohmic

RESISTANCE AND OHM’S LAW (2) The potential difference between a and b is We can rewrite the current density as Because then the potential difference The quantity is called the resistance R of the conductor The unit of R is ohm (volt/ampere)

RESISTANCE AND OHM’S LAW (3) The inverse of conductivity is resistivity

Various Resistance

A MODEL FOR ELECTRICAL CONDUCTION This models describes the connection between resistivity and electron movement in conductor. In absence of E, the electron moves randomly. The net movement is zero. Thus the drift velocity is zero (Fig. a) An E modifies the random motion and causes the electrons to drift in a direction opposite th at of E The slight curvature in the paths shown in Fig.b results from the acceleration of the electrons between collisions The acceleration of the electron is The electron will gain velocity

A MODEL FOR ELECTRICAL CONDUCTION (2) Suppose that v i =0 and is the average value of successive collision, then the drift velocity The magnitude of the current density is Comparing with ohm’s law

RESISTANCE AND TEMPERATURE The resistivity of a metal varies approximately linearly with temperature according to the expression The variation of resistance as T 0 is normally 20 o C

SUPERCONDUCTORS

ELECTRICAL ENERGY AND POWER When net positive charge moves from a to b, it gains electric potential energy. The chemical potential energy in battery decreases. As the charge travels from c to d, it losses the electric potential energy due to the collision with resistor’s atom. The rates is The energy lost in resistor is equal energy transferred by battery

ELECTRICAL ENERGY AND POWER The resistor’s voltage is, thus other formulas for energy in capacitor A battery is an emf source

Resistor in Serial Resistors connected in serial have the same flowing current 16 I = I 1 = I 2 = I 3 V = V 1 + V 2 + V 3 V I R t = I 1 R 1 + I 2 R 2 + I 3 R 3 R t = R 1 + R 2 + R 3

Resistor in Parallel Resistors in parallel have the same voltage’s magnitude  V = V 1 = V 2 = V 3  I t = I 1 + I 2 + I 3  V/R t = V/R 1 + V/R 2 + V/R 3  1/R t = 1/R 1 + 1/R 2 + 1/R 3 17 V