Transcript Resistance and Resistivity

Resistance and Resistivity
Resistance and Resistivity
Resistivity, what is it?
Resistivity is the opposite of conductivity, it’s a measure of how
effectively a material slows down the flow of electricity.
Insulators have a high resistivity rating. Materials such as metals
and other conductors have a low resistivity rating.
Resistance and Resistivity

A conductor’s Resistance is defined as the ratio of the Applied Voltage to
the Current produced.
R = V/I
Scalar
Units:
Ohm
[Ω] = [V/A]
Resistance and Resistivity


Resistance can be calculated for any object.

Good conductor – low resistance

Poor conductor –high resistance
All circuit elements have
some resistance.
The resistance of
connecting wire leads
is considered negligible.
Resistance and Resistivity
Resistance
 The geometry of the resistor matters
L
R=ρ
A
Length
Area
Resistivity: (units m)
 Increase
the Length, flow of electrons impeded
 Increase the cross-sectional Area, flow enhanced
Resistance and Resistivity
For a wire of length l and cross-sectional area A the
resistance R:
Is proportional to l
And inversely proportional to A
The constant ρ (rho)
Is known as the resistivity.
l
R
A
Resistance and Resistivity
Increasing the cross-sectional area
increases the number of available electrons.
Resistance and Resistivity
Resistance and Resistivity
Resistivity
l
R
A
Therefore, the units of resistance are:
m
R   m 2   (Ohms)
m
Resistivity has units of Ohm· meters ( · m)
Resistance and Resistivity
Resistance and Resistivity
Resistance and Resistivity
Resistivity and temperature.
The resistance and resistivity changes with temperature,
therefore resistivity at quoted at a specific temperature
The resistance is proportional to the length l and inversely
proportional to the cross-sectional area A, the material the
conductor is made from, and the temperature.
Resistance and Resistivity
Superconductivity

Below a certain critical temperature,
Resistance becomes ZERO, allowing current to exist without
energy wasted.
Superconductivity, although predicted and discovered a
century ago has only become useful recently due to the
development of rare-earth conductive ceramics.
Superconductive wires are used in the electromagnets
of MRI machines.
Resistance and Resistivity
Two wires, A and B, are made of the same metal and have
equal length, but the resistance of wire A is four times the
resistance of wire B. How do their diameters compare?
a.
b.
c.
d.
e.
dA
dA
dA
dA
dA
=
=
=
=
=
4 dB
2 dB
dB
½ dB
¼ dB
l
R
A
Resistance and Resistivity
A wire of resistance R is stretched uniformly (keeping its volume
constant) until it is twice its original length. What happens to the
resistance?
a.
it increases by a factor 4
b.
it increases by a factor 2
c.
it stays the same
d.
it decreases by a factor 2
e.
it decreases by a factor 4
Resistance and Resistivity
Find the resistance of a piece of copper with a diameter
of 1 mm and a length of 1 cm
-8
-2
l (3 x 10 )(1 x 10 ) 12
-4
R =
=
x
10

-3 2
A
(  (.5 x 10 )

Resistance and Resistivity
Bolbo the gold broker from Baghdad has just received a gold
bullion bar for his birthday from his brother Bob. The face of the
bar is 5 cm on both sides, and the length is 20 cm. The resistance
between faces A and B is measured to be 0.8 micro-ohms. Bolbo
the broker assumes that the bullion is gold if the measured
resistance is within +/- 10% of the theoretical value. Is the material
gold or is it bogus?
R  L / A
 (2.4 x108   m)(.2m) / .052 m 2 )
 1.92 x106 
=1.92 u don’t try to cash it in!
B
Resistance and Resistivity
A wire 10 m long consists of 5 m of copper followed by 5 m of
aluminum of equal diameter of 1 mm. A voltage difference of 80 V
is placed across the composite wire.
a.
What is the total resistance of the wire?
b.
What is the current flow through the wire?
Resistance and Resistivity
Summary