Transcript Electrical Resistance and Resistivity

Electrical
Resistance and
Resistivity
What IS Resistance?
On what will resistance depend?

A measure of how
easily charge flows
through a material

A Resistor is a
material of significant
resistance that has
been placed in an
electric circuit in order
to control current or
voltage
On what will a wire’s resistance depend?

There are 4 primary factors when
determining a wire’s resistance:
 Material
 Length
composition
of the wire
 Cross-sectional
 Temperature

HOW?
 Turn
and talk!
Area of the wire
Question 17.3a
Wires I
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 = 4dB
b) dA = 2dB
c) dA = dB
d) dA = 1/2dB
e) dA = 1/4dB
Resistivity (r) of a wire

A physical property of the wire that depends on the
material of which the wire is constructed; determines how
easily current can flow through the material

When the temperature is CONSTANT:
l
Rr
A

Units = W·m

Conductivity (s) is the inverse of resistivity
Question 17.3a
Wires I—try again 
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 = 4dB
b) dA = 2dB
c) dA = dB
d) dA = 1/2dB
e) dA = 1/4dB
Question 17.3a
Wires I
Two wires, A and B, are made of
a) dA = 4dB
the same metal and have equal
b) dA = 2dB
length, but the resistance of
wire A is four times the
c) dA = dB
resistance of wire B. How do
d) dA = 1/2dB
their diameters compare?
e) dA = 1/4dB
The resistance of wire A is greater because its area is less than
wire B. Since area is related to radius (or diameter) squared, the
diameter of A must be two times less than the diameter of B.
l
Rr
A
Question 17.3b
Wires II
A wire of resistance R is stretched
a) it decreases by a factor of 4
uniformly (keeping its volume
b) it decreases by a factor of 2
constant) until it is twice its original
c) it stays the same
length. What happens to the
d) it increases by a factor of 2
resistance?
e) it increases by a factor of 4
Question 17.3b
Wires II
A wire of resistance R is stretched
a) it decreases by a factor of 4
uniformly (keeping its volume
b) it decreases by a factor of 2
constant) until it is twice its original
c) it stays the same
length. What happens to the
d) it increases by a factor of 2
resistance?
e) it increases by a factor of 4
Keeping the volume (= area x length) constant means
that if the length is doubled, the area is halved.
l
R

r
Since
A , this increases the resistance by a
factor of 4.
Resistivities for Common
Conductive Materials (table 17.1)
Practice Problem!

What is the resistance of a piece of copper
wire that is 10.0 m long and 1.2 mm in
diameter (r=1.70 x 10-8 W·m)?
L  10.0m
r  0.6mm  0.0006m
rL
rL
R

2
A  r
r  1.70 108 W  m
8
(1.70 10 )(10.0)
R
2
  (0.0006)
R  0.15 W
Temperature effect on R

Would you expect a higher
temperature to cause an INCREASE
or a DECREASE in the resistance of a
wire? Why?
Temperature effect on R

Temperature increases causes
resistance to increase:
R f  R0 (1  a t )



R0 = resistance at some reference
temperature
Rf = resistance at some temperature t
(in °C) above the reference
temperature
a = temperature coefficient for
material
Resistors

Items placed in an electrical circuit in order to limit
the current that can flow.

Made of a (relatively) conductive carbon-composition
core, with wires embedded on either end.

In the picture, you can see a cutaway showing the
insides of some resistors.

Which do you think has the highest resistance?
Why?
Measuring Resistance

Units = Ohm (W)

Multimeter: A tool designed to measure
multiple electrical quantities, such as
resistance, AC and DC current, AC and DC
voltage, and capacitance.

Color Code:

Each band represents a value in the
overall resistance

Each Color represents a different number
Resistor Color Code
COLOR
VALUE
Black
0
Brown
1
Red
2
Orange
3
Yellow
4
Green
5
Blue
6
Violet
7
Grey
8
White
9
Effective Resistance: Series
Resistors in Series: Example

Given the following information, what is the effective
resistance of this series of resistors:
R1  425 W
R2  1.50 kW
R3  323 W
Reff  Ri  (425)  (15 0 0)  (323)
Reff  2248 W  2250 W
Effective Resistance: Parallel

The effective resistance will be smaller
than the lowest resistance in the parallel
combination
Resistors in Parallel: Example

Determine the effective resistance of this parallel configuration of
resistors:
1
1
1
1
1
 


Reff
Ri 150 210 175
R1  150 W
R2  210 W
R3  175 W
1
7
5
6
18




Reff 1050 1050 1050 1050
Reff
1050

 58.3 W  58 W
18
Daily Wrap-up!


Covered today:

Resistivity

Resistors in Series and Parallel
Due Tomorrow:

Lab: Resistors and Resistance