# Ohm�s Law and Resistance by a74QIjce

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```									Ohm’s Law and
Resistance

AP Physics C
Montwood High School
R. Casao
Current Density J
• For a conductor of cross-sectional area
A carrying current I, the current
density J is:

I
J    n  q  vd
A
• The current density is in the direction
of motion of the charges for positive
charge carriers and opposite the
direction of motion for negative charge
carriers.
Ohm’s Law
• A current density J and an electric
field E are established in a conductor
when a potential difference is
maintained across the conductor.
– If the potential difference is constant, the
current in the conductor will also be
constant.
• Ohm’s law: J = ·E
 = conductivity
Ohm’s Law
• Ohm’s law states that for many
materials (including most metals), the
ration of the current density and
electric field is a constant , which is
independent of the electric field
producing the current.
• The most common form of Ohm’s law
is:
V
I
R
Resistance
• The motion of a ball
rolling down an
inclined plane and
bouncing off pegs in
its path is
analogous to the
motion of an
electron in a
metallic conductor
with an electric field
present.
Resistance
• If some of the pegs were removed, the ball
would experience less resistance to its
movement. If more pegs were added the ball
might experience more resistance to its
downhill motion.
•   At the atomic level, currents are pictured as
the flow of the outer electrons of atoms
through the material.
•   Resistance results from collisions of
electrons with other electrons and with
atoms.
•   Resistance is the opposition to the flow of
charge in a conductor.
Resistance
1V
• Resistance is measured in ohms .       1Ω 
1A
• The inverse of the conductivity  of a material is its
resistivity ; units ·m.
1
ρ
σ
• Resistivity is related to the nature of the material.
Good conductors have low resistivity (or high
conductivity). Poor conductors have high
resistivity (or low conductivity).
• Resistance:                 Resistivity:
ρl
R             = o + o ··(T – To)
A
Resistance
• The resistance of a conductor is proportional to the
length.
– Resistance increases with increased length.
• The resistance of a conductor is inversely
proportional to the cross-sectional area of the
conductor.
– Resistance decreases with increased cross-
sectional area.
• Resistance is also dependent upon the temperature
of the conductor. Collisions of electrons with other
electrons and with atoms raises the temperature of
a material as the added heat energy causes the
electrons to move faster and hence collide more
often. This increases the resistance of the
conductor.
Factors Affecting Resistance
Resistance and Temperature
• R = Ro· + Ro··(T – To)
•  is the temperature coefficient of
resistivity.
• All electric appliances have a fixed
resistance.
• Electric circuits make use of resistors
to control the current level in the
circuit.
Web Sites

• Resistors and Resistor Color Code
Calculator
• Resistor Color Code
• Ohm’s Law
• Voltage Circuit Simulator

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