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
• Resistance is measured in ohms .
1V
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
A
 = o + o ··(T – To)
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 crosssectional 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