1. Introduction to Electrical & Computer Engineering Ohm’s Law
Dr. Cynthia Furse
University of Utah
Dr. Cynthia Furse
University of Utah

2. Ohm’s Law Voltage = Current x Resistance (V=IR) What is Resistance ?
Conductivity
Resistivity
Resistance
Resistance is used for:
Control of Voltage & Current
Sensing of physical properties
I-V Curves

3. Ideal Voltage and Current Sourcesis is + - - vs

4. + + + + + Voltage = Potential
Think of Voltage as a ‘stack of positive charges’
at the top of a hill.
It has Potential Energy! + + a + +
Vab b

5. Current = Flow is

6. Resistance to Flow of Current
Voltage and current are the fundamental elements of electricity. Resistance relates voltage and current through the familiar ‘Ohm’s Law’. V= I R.
Resistors work the same way whether the voltage and current are AC or DC. There is no polarity associated with a resistor, only with the voltages and currents. There is also no right or wrong ‘side’ to a resistor. You can turn them around (top to bottom, in this picture), and they act just the same.
The colored bands on the resistor are a code for the value of resistance and its tolerance. See ‘Resistor Color Code’ in the reference material for more information.
Remember on our first card, I said ‘ELECTRICAL ENGINEERING is about what you can do to a voltage (or current)?’ So … if you have a fixed voltage (like a battery), and you change the resistance, you will then change the current.
R (Ω)
R (Ω)

7. Water-Circuit Analogy
Voltage
(Potential)
Resistance
(Rocks/Pipes)
Current
(Flow)

8. Ohm’s Law: v = i R i
R (Ω) + - - v

9. Ohm’s Law: v = i R i=10A R= 1Ω or 2 Ω + - - v
How much voltage required to drive 10 A through 1 Ω resistor?
V = (10A) (1 Ω) = 10V
How about for a 2 Ω resistor?
V = (10A)(2 Ω) = 20V
For a constant current, more resistance requires more voltage

10. Ohm’s Law: v = i R i V=10V R= 1Ω or 2 Ω + - -
How much current will a 10V source drive thru a 1Ω resistor?
I = V/R = (10V) / (1 Ω) = 10A
How about for a 2 Ω resistor?
I = (10V)/(2 Ω) = 5A
For a constant voltage, higher resistance reduces the current.

11. Ohm’s Law: v = i R I = 10A V=10V R + - -
For a 10V, 10A source, what is the resistance?
R = V/ I= (10V) / (10A) = 1 Ω
How about for a 5A source?
R = (10V)/(5A) = 2 Ω
Measuring V & I can tell us R. R is often used as a sensor.

12. Resistor Color Codes
All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press
Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press, Used with Permission by the Publisher

13. I-V Curves used for diagnosis, design, etc.
Current (I)
R=1kΩ
1mA
V R
0.5mA
R=2kΩ
R= ∞ 1V
Voltage (V)
V = I R

14. I-V Curves for LED (Vf is where light turns on)

15. Resistance (R) and Resistivity (ρ)
Resistance: ability to resist flow of electric current
Resistance (R ) Ω (ohms)
Resistivity (r) Ω/m (ohm-meters)
Conductivity (σ ) m/Ω -1
All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press
Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press, Used with Permission by the Publisher

16. Resistance can be used as a sensor Measuring Resistance of Sea Ice

17. Other Resistive Sensors
Thermistor = R changes with Temperature
Piezoresistor = R changes with Strain or Pressure
Light-dependent
Resistor (LDR) =
R changes with light
Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press, Used with Permission by the Publisher

18. Conductivity
Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press, Used with Permission by the Publisher

19. Superconductivity
Critical temperature TC is the temperature at which a material becomes superconducting (zero resistance & no power dissipation)
Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press, Used with Permission by the Publisher

20. Resistance can be used to control Voltage and Current
Variable Resistor. See page 44 of your textbook.
On our last card, we said that if you have a fixed voltage, changing the resistance can change the current. Or if you have a fixed current, you can change the voltage. Resistance relates voltage and current through the familiar ‘Ohm’s Law’. V= I R. So, selecting / controlling / changing the resistance is one way that we control the voltage or current in our circuits.
There are several ways to control the resistance.
Choose a resistor value (see standard resistor values in the reference material)
Use a variable resistor, and ‘dial’ the resistance you want. (
Potentiometer: 3-terminal variable resistor. Connect to the middle and one side leg. The two outside legs will be the full resistance, regardless of where the dial is set.
Rheostat: 2-terminal variable resistor
There are also several types of sensors where the resistance changes depending on what you are trying to sense.
Temperature – Thermister
Pressure – Piezoresistor
Light intensity – Light-dependent R (LDR)
Thank you to the following website for the picture of how a round potentiometer works:

21. Variable Resistors
Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press, Used with Permission by the Publisher

22. Conclusion -- Ohm’s Law
Voltage = Current x Resistance (V=IR)
What is Resistance ?
Conductivity
Resistivity
Resistance
Resistance is used for:
Control of Voltage & Current
Sensing of physical properties
I-V Curves

23. Dr. Cynthia Furse University of Utah
Introduction to Electrical & Computer Engineering Antelope Island, Great Salt Lake, Utah
Dr. Cynthia Furse
University of Utah