1. Introduction to Electrical & Computer Engineering Voltage & Power
Dr. Cynthia Furse
University of Utah

2. Introduction to Electrical Engineering Voltage & Power
What is voltage?
How do you measure it?
Polarity
Ground
What is Power? Energy?
Getting Real.

3. Voltage = Energy to move 1 unit of negative charge e- from a to b
Vab b

4. Voltage = Energy to move 1 unit of positive charge e from b to a+ e
Vab b

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

6. Voltage is a potential difference measured between two points
Vab =
1.5 V
Means …
Va is 1.5 V
Higher than Vb + a
VΩ com A
Vab b -
DVM

7. Voltage polarity: What if I switch?
Vba =
-1.5 V
Means …
Vb is 1.5 V
lower than Va + a
VΩ com A
Vab b -
DVM

8. Voltage is Measured Relative to Ground / Reference / Neutral
Voltage is always defined relative to a ‘ground’ or reference point. In a house, for example, the electrical system is grounded to ‘earth ground’. This is also sometimes called the ‘neutral’ point in the circuit. A copper rod (or several) are driven into the earth outside of the house, and are connected to the electrical system with heavy copper wire. The voltage at the ground point is ‘zero’. All current flows into this ground point. Two common symbols for ground are shown here. You will always need to ONE of these ground reference points in your system. All voltages will then be calculated relative to this point.

9. R1 (Ω) Va I
Va-Vb=
Vab
=1.5V
R2 (Ω)
Vc=? Vb

10. Va=? I Va-Vb= Vab =1.5V Vc=? Vb=? Vg=0 R=1kΩ R=1kΩ Va –Vb = 1.5V
If R1=R2 then Vc = half of Vab= 0.75 V
Va = 1.5V
Vb = 0V
Vac = Va – Vc = 0.75 V
Vbc = Vb-Vc = -0.75V
Check with multisim
Vb=?
Vg=0

11. Va =? I Vc=? Va-Vb= Vg=0 Vab =1.5V Vb=? R=1kΩ R=1kΩ Va –Vb = 1.5V
Now Vc = 0 V
Vac = Va – Vc = 0.75 V still
Vbc = Vb-Vc = -0.75V still
So … Va = 0.75V
Vb = -0.75V
Check with multisim
Vb=?

12. What is a really BIG voltage?
High Voltage Lines = 110 kV +
Residential
240 V / 120 V
Lightning = 1 Billion
(1 x 10 ^9) V

13. What is a really SMALL voltage?
Neuron Action Potential =
- 55 mV
Cardiac Action
Potentials
-100 to + 50 mV
Bird on transmission line:
Bird on a line
10 mV

14. Utah Electrode Array

15. Power (Watts)

16. Passive Sign Convention
Vab a b
Current into device (I) + -
P = (Vab)(I) If P > 0 device consumes power
If P < 0 device produces power

17. + - + I=V/R =1.5mA Vr=IR =1.5V - V= -1.5V - + Vg=0 R=1kΩ Va –Vb = 1.5V
If R1=R2 then Vc = half of Vab= 0.75 V
Va = 1.5V
Vb = 0V
Vac = Va – Vc = 0.75 V
Vbc = Vb-Vc = -0.75V
Check with multisim - +
Vg=0

18. + - + I=V/R =1.5mA Vr=IR =1.5V - V= -1.5V - +
R=1kΩ +
I=V/R
=1.5mA
Vr=IR
=1.5V -
V= -1.5V
Va –Vb = 1.5V
If R1=R2 then Vc = half of Vab= 0.75 V
Va = 1.5V
Vb = 0V
Vac = Va – Vc = 0.75 V
Vbc = Vb-Vc = -0.75V
Check with multisim - +
Vg=0
P = (-1.5V)(1.5mA) = -2.25mW
P = (1.5V)(1.5mA) =2.25mW

19. Energy (Joules or kWh)

20. How Much Energy Do You Need??
Efficient Appliances? (kWatts)
# of hours? (hours)
Multiply, Sum = kWh
Recharge time? (night, dark/snow days)

21. Introduction to Electrical Engineering Voltage & Power
What is voltage?
How do you measure it?
Polarity
Ground
What is Power? Energy?
Getting Real.

22. Introduction to Electrical & Computer Engineering Voltage & Power
Solar Powered
Neighborhood
Internet Base station
Emigration Canyon, Utah
Dr. Cynthia Furse
University of Utah