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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
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
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
16
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