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

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

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

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

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

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

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

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.

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

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

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=?

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

What is a really SMALL voltage? Neuron Action Potential = - 55 mV Cardiac Action Potentials -100 to + 50 mV Bird on transmission line: http://van.physics.illinois.edu/qa/listing.php?id=15327 Bird on a line 10 mV

Utah Electrode Array

Power (Watts)  

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

+ - + 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

+ - + 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

Energy (Joules or kWh)  

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

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

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