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 perpendicular 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 conductor 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

x A x

nA x

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 vd

is an average speed called the drift speed

dv

tdx v t

RESISTANCE AND OHM’S LAW

• We know that average current is

• The current density J

• In some materials, the current density is proportional 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)

/J I A

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 that 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 vi=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

• T0 is normally 20o 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

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Resistor in Serial

• Resistors connected in serial have the same flowing current

I = I1 = I2 = I3

V = V1 + V2 + V3

V I Rt = I1R1 + I2R2 + I3R3

Rt = R1 + R2 + R3

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Resistor in Parallel• Resistors in parallel have the same voltage’s magnitude

V = V1 = V2 = V3

It = I1 + I2 + I3

V/Rt = V/R1 + V/R2 + V/R3

1/Rt = 1/R1 + 1/R2 + 1/R3

V