Transcript Ohm`s Law - comm

Ohm’s Law
Explanation and Verification
Brett MacDonald
Andrew Misquita
Michael Ramsay
Dec.15/09
Agenda
1. Introduction
2. Principles of Ohm’s Law
3. Verifying Ohm’s Law
4. Summary
Introduction
• Background
• Purpose
• Methodology
Background
• Ohm’s law was created in 1827 by Georg
Ohm
• It is one of the most widely used and
recognized laws
• Very important basis of all electronic and
electrical systems
• Has remained unchanged for almost 200
years
Ohm’s Law deals primarily with the values of:
V = Potential Difference (Volts)
I = Current (Amps)
R = Resistance (Ohms)
Ω = Universal symbol for Ohms
E
I
R
E  IR
E
R
I
Common terms used:
Potential Difference (Volts) - Difference in charge (positive and
negative) between two separated points.
Current (Amps) – The flow of charge in a circuit, per unit of time.
Resistance (Ohms) – A measure of the opposition to current
flowing through a circuit.
Series Circuit – An electric current that passes through every
component of a circuit without splitting up into separate sections
Parallel Circuit – An electric current that splits up due to several
components that have a point in common.
Purpose
• Verify Ohm’s Law
• Explain how it works
• Demonstrate it in
real circuits
Methodology
Sources Used:
•
•
•
•
Books
Internet
Textbooks
Experimentation
Please note: The experiments performed
were not meant to make discoveries or find new
concepts, they are simply used to prove and verify
Ohm’s Law
Principles of
Ohm’s Law
• History of Georg Ohm
• Explanation of Ohm’s law
• Application in Industry
History of Georg Ohm
• Was born March 16, 1789 in Erlangen Germany
• Started career as a mathematics instructor
• Wrote an elementary book on geometry in 1812
• As a reward Georg was later sent to work at Jesuit
Gymnasium of Cologne in 1817 to teach
mathematics and physics
• Sophisticated equipment and instruments available to him in this
school, allowed him to further his understanding of physical and
mathematical principles
• His law first appeared in the book titled Die Galvanische Kette
Mathematisch Bearbeite. (English translation: The Galvanic Circuit
Investigated Mathematically)
• The book started with basic mathematics and then continued into his
new theories of electrical properties.
• One of these properties was the proportionality of current, and
voltage in a resistor, Ohm’s Law.
• He also adopted the unit of resistance, the Ohm.
Explanation of Ohm’s Law
When looking at physical systems, there is a basic concept that holds
true for almost any situation involving a change.
Cause
Effect 
Opposition
Ohm's law is a great example of how this relationship works.
Cause
Effect 
Opposition
PotentialDifference
Current 
Resistance
Any change to potential difference, current, or resistance has a direct
and linear effect on the other two quantities.
Consider current plotted as a function of time, with a fixed resistance.
As the voltage increases, the current should increase linearly and in a
straight line.
Current as a Function of Voltage with a Fixed Resistance
(5 Ohms)
16
14
A
12
10
8
6
4
2
0
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
Using point A on the diagram above, Ohm’s Law can be used to find
resistance and verify the results.
At this point, current is 8 Amps, and potential difference is 40 Volts. If
Ohm’s law is rearranged to solve for resistance we should get a value
of 5 Ohms.
E
I
R
E
R
I
40Volts
R
8 Amps
R  5Ω
This simple calculation is proof of Ohm’s law, although it is important to
take into consideration that this is a very basic example of the
relationship.
Application
• Ohm’s law is used extensively in circuit analysis to find unknown
quantities
• Most commonly used in the work force by electrical and electronic
engineers
• Used in the design process of any appliance consisting of electric
components
Some jobs that would require
knowledge of Ohm’s Law:
•
•
•
•
Car audio installation
Designing city power grids
Electronic repair jobs
Installation of home power supplies
[3]
Verification of
Ohm’s Law
• Experimental Design
• Predicted and Measured Values
• Analysis
Experimental Design
In this experiment, 2 types of circuits were tested
(Series and Parallel)
Series configuration:
Parallel Configuration:
In these experiments, Ohm’s Law will be used to
calculate the predicted values in each circuit.
For the series circuit it will be used to predict:
• Total current
• Voltage drop across each resistor
For the parallel circuit it will be used to predict:
• Current across each parallel branch
[4]
Series Circuit
Measured
Value
8.85 kΩ
Percent Error (%)
R Total
Predicted
Value
9 kΩ
I Total
2.2mA
2.23mA
1.36%
Voltage drop across
R1
Voltage drop across
R2
Voltage drop across
R3
2.2V
2.23V
1.36%
10.34V
10.23V
-1.06%
7.26V
7.34V
1.10%
-1.67%
Parallel Circuit
R total
Predicted
Value
660Ω
Measured
Value
654Ω
Percent Error
(%)
-0.91%
Current across R1
20mA
20.3mA
1.5%
Current across R2
4.26mA
4.34mA
1.88%
Current across R3
6.06mA
6.06mA
0%
Analysis
After completing the experiment it was found that the predicted
values were extremely close to the measured values, not exceeding
percent error of more than ±2%.
Due to the accuracy of these values, this experiment verifies that
Ohm’s Law holds true for both parallel and series circuits. No further
calculations or analysis is needed.
Possible Source of Error: fluctuating resistor values
Summary
The purpose of this presentation was to verify, explain,
And demonstrate Ohm’s Law. In the first main section
Titled “Principles of Ohm’s Law”, the law was explained
using the analogy that effect in a physical system is
equal to the cause divided by its opposition. The effect
would be the flow of charge, or current produced by the
circuit. The cause would be the applied voltage, or
potential difference introduced, and the opposition to that
flow of charge would be the total resistance of the circuit.
In the second section titled “Verification of Ohm’s Law” the
law was verified using experimentation. The law was
tested on both series and parallel circuits. Due to the
Very minor discrepancy between the predicted and
Measured values, the final outcome of the experiment
verified that Ohm’s Law holds true for both series and
parallel circuits.
References
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http://www.qcas.net.au/images/Graphics%20GIF/33_books.gif. [Accessed Dec. 5/09].
[2] BDEG, “Goerg Ohm” 2005. [Online]. Available: http://bdeg.sopron.hu/~spider/Ohm.jpg. [Accessed Dec. 5/09].
[3] XJTAG, “Images” 2006. [Online]. Available: http://www.xjtag.com/images/press/30-03-06c.jpg. [Accessed Dec.
7/09].
[4] modyoursystem, “Pics” 2007. [Online]. Available: http://www.modyoursystem.com/pics/multimeter.jpg. [Accessed
Dec. 12/09].
R. L. Boylestead, “Ohm’s Law, Power and Energy” in Introductory Circuit Analysis: eleventh edition, V. Anthony, R.
Davidson, and L. Dimmick, Ed., Upper Saddle River, NJ: Pearson Prentice Hall, 2007, pp. 101-105..
Wikipedia, "Ohm's Law" 2009. [Online]. Available: http://en.wikipedia.org/wiki/Ohm's_law. [Accessed Nov.
24, 2009].
Wikipedia, "Georg Simon Ohm" 2009. [Online]. Available: http://en.wikipedia.org/wiki/Georg_ohm.
[Accessed Nov. 27, 2009].
Physics, "Ohm's Law" 2009. [Online]. Available:
http://www.physics.uoguelph.ca/tutorials/ohm/Q.ohm.intro.html. [Accessed Nov. 30, 2009].
All About Circuits, "How Voltage, Current, and Resistance Relate" 2009. [Online]. Available:
http://www.allaboutcircuits.com/vol_1/chpt_2/1.html. [Accessed Dec. 1, 2009].