CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE...
Transcript of CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE...
![Page 1: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/1.jpg)
1
CHAPTER 25
CURRENT, RESISTANCE AND
ELECTROMOTIVE FORCE
BASIC CONCEPTS
CURRENT and CURRENT DENSITY
RESISTANCE and RESISTIVITY
BATTERY INTERNAL RESISTANCE
ENERGY AND POWER IN CIRCUITS
![Page 2: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/2.jpg)
2
CURRENT IS THE MOVEMENT OF CHARGE
IN A MATERIAL
In some cases the objects that are moving
are positive.
![Page 3: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/3.jpg)
3
In other cases, for example in metals, the
objects are negative (electrons).
![Page 4: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/4.jpg)
4
Current is the time rate of passage of the
charge.
![Page 5: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/5.jpg)
5
Consider that there are n moving charged
particles per volume
And
The average drift velocity is vd
Then in time dt
The particles move a distance of vddt
In the volume, Avddt, shown in the figure
there will be nAvddt particles.
Each particle has a charge q.
Thus in time dt the charge, dQ, that will
pass through the cylinder is
![Page 6: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/6.jpg)
6
Current is
Current density (current per unit cross‐
section of the conductor) is
Note that current density is a vector
![Page 7: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/7.jpg)
7
RESISTIVITY
Resistivity, ρ, is a characteristic of a
material.
![Page 8: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/8.jpg)
8
RESISTIVITY
Resistivity, ρ, changes with temperature.
Where is the value at 200 C.
![Page 9: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/9.jpg)
9
For a metal:
![Page 10: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/10.jpg)
10
For Semiconductor:
![Page 11: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/11.jpg)
11
Some materials loose all resistivity –
Superconductors:
Discovered in 1911 by H. Kammerlingh
Onnes.
![Page 12: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/12.jpg)
12
RESISTANCE
Resistance is a characteristic of an object.
Resistance, R, is related to Resistivity, ρ, by
![Page 13: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/13.jpg)
13
The longer the object the higher the
resistance.
The larger the cross‐section the smaller the
resistance.
If ρ is constant the total current through a
conductor is proportional to the voltage
across it.
Or
![Page 14: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/14.jpg)
14
The constant of proportionality is the
resistance, R.
Or
This is Ohm’s Law.
If a resistor obeys Ohm’s Law it is an Ohmic
resistor.
![Page 15: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/15.jpg)
15
Obeys Ohm’s Law:
![Page 16: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/16.jpg)
16
Semiconductors are not Ohmic:
![Page 17: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/17.jpg)
17
POWER DISIPATED WITH CURRENT FLOW.
Remember
q
V
Change in energy
![Page 18: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/18.jpg)
18
And
Therefore
Use Ohm’s Law
![Page 19: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/19.jpg)
19
Or
![Page 20: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/20.jpg)
20
CALCULATE RESISTANCE
A copper rod with cross section A has a
length L what is its resistance? Work for
and .
From Table 25.1
Therefore
![Page 21: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/21.jpg)
21
More difficult: Example 25.4
A cylinder with resistivity ρ has length L,
inner radius a and outer radius b. Calculate
the resistance for current flow from the
inner to the outer walls.
![Page 22: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/22.jpg)
22
Where is the path length of the current
flow.
And is the cross‐section for current flow.
Now
Consider a thin shell within the cylinder wall
with radius , thickness and length .
The area of the shell is .
The path the current flows is .
![Page 23: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/23.jpg)
23
Then
Integrate to get .
![Page 24: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/24.jpg)
24
CIRCUITS
Circuit elements:
![Page 25: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/25.jpg)
25
Other symbols will be added after we
discuss magnetism.
Internal Resistance
Two points:
If no current is in a circuit element there is
no potential drop across the element.
Batteries have internal resistance.
![Page 26: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/26.jpg)
26
The figure is of a 12 V battery with no
current in the circuit.
The voltmeter will read 12 V.
But if there is current:
![Page 27: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/27.jpg)
27
The voltmeter will read less than 12 V.
What is the current in the circuit?
![Page 28: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume](https://reader033.fdocuments.us/reader033/viewer/2022042217/5ec250c0d59c9109e348e530/html5/thumbnails/28.jpg)
28
What will the voltmeter read?