Electrical Resistance and

ResistivitySyllabus Statements 5.1.6-5.1.7, 5.2.3

We are in chapter 17 of your textbook!

What IS Resistance?On what will resistance depend?

On what will a wire’s resistance depend?

There are 4 primary factors when determining a wire’s resistance: Material composition Length of the wire Cross-sectional Area of the wire Temperature

HOW? Turn and talk!

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:

Units = W·m

Conductivity (s) is the inverse of resistivity

lR

A

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

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.

Question 17.3a Wires ITwo 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

lR

A

Question 17.3b Wires II

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 decreases by a factor

of 4

b) it decreases by a factor

of 2

c) it stays the same

d) it increases by a factor

of 2

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.

Since , this increases the resistance

by a factor of 4.

Question 17.3b Wires II

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 decreases by a factor

of 4

b) it decreases by a factor

of 2

c) it stays the same

d) it increases by a factor

of 2

e) it increases by a factor

of 4

lR

A

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?

2r

L

A

LR

m

mmmr

mL

81070.1

0006.06.0

0.10

150.0

)0006.0(

)0.10)(1070.1(2

8

R

R

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:

R0 = resistance at some reference temperature

Rf = resistance at some temperature t (in °C) above the reference temperature

a = temperature coefficient for material

0 (1 )fR R t

Effective Resistance: Series

Resistors in Series: Example Given the following information, what is the

effective resistance of this series of resistors:

323

k 50.1

425

3

2

1

R

R

R

2250 2248

)323()0015()425(

eff

ieff

R

RR

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:

175

210

150

3

2

1

R

R

R

58 3.5818

1050

1050

18

1050

6

1050

5

1050

71

175

1

210

1

150

111

eff

eff

ieff

R

R

RR

Daily Wrap-up!

Covered today:

Resistivity

Resistors in Series and Parallel

Due Tomorrow:

Lab: Resistors and Resistance