Resistivity and Resistance

1. Resistance and Resistivity

2. 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.

3. 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]

4. 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.

5. Resistance and Resistivity
Resistance
 The geometry of the resistor matters
L
R=ρ
A
 Increase the Length, flow of electrons impeded
 Increase the cross-sectional Area, flow enhanced
Resistivity: (units m)
Length
Area

6. 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



7. Resistance and Resistivity
Increasing the cross-sectional area
increases the number of available electrons.

8. Resistance and Resistivity

9. Resistance and Resistivity
Resistivity
2
( )
m
R m Ohms
m
   
l
R
A


Resistivity has units of Ohm· meters ( · m)
Therefore, the units of resistance are:

10. Resistance and Resistivity

11. Resistance and Resistivity

12. 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.

13. 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.

14. 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. dA = 4 dB
b. dA = 2 dB
c. dA = dB
d. dA = ½ dB
e. dA = ¼ dB
l
R
A



15. 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

16. 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
-4
-3 2
(3 x 10 )(1 x 10 ) 12
= = x 10
( (.5 x 10 )
l
R
A

 
 


17. 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?
B
8 2 2
6
/
(2.4 10 )(.2 ) /.05 )
1.92 10
R L A
x m m m
x




 
 
=1.92 u don’t try to cash it in!

18. 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?

19. Resistance and Resistivity
Summary