Welcome to Introduction to Electrical and
Computer Engineering at the University of Utah.
I am Dr. Cynthia Furse, and today, we'll be talking about voltage and power.
If you have ever wanted to live off the grid, or
if you need an internet base station in a remote area, or perhaps you just want to
be able to charge up the batteries on your RV, this lecture is for you.
We're going to talk about what is voltage,
how do you measure it, what's the polarity, ground, what's power,
what's energy, and then let's get real with some interesting applications.
Voltage is the energy that's required to move one unit of negative charge,
e minus, to point a to point b.
Another way to think of this is it's the same energy that's required to lift
one unit of positive charge e from point b to point a.
That's the way I like to think about it.
Voltage is equal to potential.
Think of the voltage as a stack of positive charges
at the top of a hill at point a.
This has potential energy.
Voltages are potential differences measured between two points.
You can see the voltmeter here who we've connected the positive red lead onto a and
the common or negative ground lead onto b.
V from point a to point b, or Vab, this include the 1.5 volts.
That means that Va is 1.5 volts higher than Vb.
Voltage has polarity.
What if I switch my leads?
What if I measure with a red lead at point b and a negative lead at point a?
Then Vba will be read on the volt meter as -1.5 volts.
That means that Vb is 1.5 volts lower than Va.
You could stop for a minute, if you like, and use Multisim to be able to experiment
with your voltage and your voltmeter to be able to see this happen.
Voltage is always measured relative to a ground.
We also call that the reference or the neutral.
Here are two cards that show you what symbols we might use for ground.
We always define the voltage of the ground as being 0 volts.
Here's an example of a very simple circuit.
This is where we have a battery.
It's connected onto two resistors.
And we might be interested in knowing, what is Vc in-between these two resistors?
Well, we can tell one thing about this particular picture.
We know that Vab is 1.5 volts because I bought a 1.5 volt battery.
But without having a ground, I can't tell you exactly what Vc is.
So let's define the ground at a place that's convenient to us.
For me, the most convenient place is at the bottom of the battery, so
I'm going to install my ground right here at this point.
Then I can say, what's Va, what's Vb, and what's Vc?
Let's start with Vb, that's the easiest.
Okay, check this out.
Vb is directly connected onto the ground, so I know that Vb is 0 volts.
That's my definition.
I'm gonna use three lines to say Vb is defined as zero
because that's where I put my ground.
Now, what about Va?
Remember that Va is 1.5 volts above Vb,
Vb is zero, so Va is 1.5 volts.
Now, what about Vc?
We can see that these two resistors are equal.
That means that the voltage is going to be evenly split between them.
The voltage between this point right here and the bottom, which is 0, is 1.5 volts.
So Vc is going to be halfway in between 1.5 volts and 0,
where it's going to be 0.75 volts.
Now, this particular definition of Va, Vb, and
Vc is totally dependent on where I placed my ground.
Let me show you what I mean.
Let's go choose a different ground point.
This time, let's put our ground right here in-between the two resistors.
It's legal, we can go ahead and do that.
It may not be quite as convenient, but let's see what happens.
Okay, Vc is at the point of the ground.
So remember, the ground defines our voltage as being 0, so Vc is equal to 0.
Now, what about Va and Vb?
Well, we know that Va is 1.5 volts higher than Vb.
And how about its relationship to Vc?
Well, because we originally split the voltage here,
we're going to still be splitting the voltage, so we can see that
Va is going to be 0.75 volts higher than Vc, so Va is going to be 0.75 volts.
All right, what about Vb?
Well, that's going to be 0.75 volts lower than Vc,
so that's going to be -0.75 volts.
Let's kinda check ourselves.
We know that Vab has to be 1.5 volts, is that going to be true?
Va is 0.75 volts, Vb is -0.75 volts, so
absolutely, we got our 1.5 volts.
Now, notice that the relative voltages in this circuit are the same as they were
before when we had our ground at the bottom, but
the absolute values of these voltages are different.
Does it matter?
The answer is no.
Everything in my circuit can be relative to the ground at any location, and
I can do my calculations accordingly.
So it doesn't matter where I put my ground
except that I'm most often going to choose it for my calculation convenience.
Okay, let's go on to the next idea.
Let's talk about some real stuff.
So what's a really big voltage, and what's a really little voltage?
Let's have some ideas in mind so that when we do our calculations,
our math, we have an idea if we're getting something that's reasonable.
The biggest voltage that I could find in nature is lightning.
It's not uncommon for lightning to have 1 billion volts.
That's one times tenth to the ninth, that is really big voltage.
There's some interesting information on lightning in the reference material at
the end of this lecture.
High voltage lines also have large voltage.
High voltage lines are often 110 kilovolts or higher, and indeed,
they are considered high voltage.
Your house, your residential construction has 240 volts for
your largest appliances and 120 for most of your general use.
Now, what's a really small voltage?
Neural action potentials, the electric potential that stimulates a single neuron,
is a relatively small voltage.
That's about -55 millivolts.
Your cardiac action potential is about the same range, that's -100 to +50 millivolts.
A bird sitting on a power line is another example of a very small voltage.
We say the bird can sit on the line without being shocked
because it has no potential difference.
It's not exactly right.
Has a very small potential difference of about 10 millivolts between the left and
the right leg, and that is small enough that it doesn't hurt the bird.
There's some very interesting research going on at the University of Utah
relative to electrodes and neurons that you might be very interested in.
The Utah electrode array is a very small array made from silicone that has ten
electrodes by ten electrodes.
Each electrode is like a tiny needle.
It's made from silicon, it is conductive, it's connected to an individual line.
If you look at this big kind of gold line right here, that has 100 little different
lines, about [INAUDIBLE] of hair that come back to a central system.
This electrode array can be placed in or in contact with any nerve.
For example, it could be stuck on the surface of the brain.
This can be used to either receive from the nerves and
be able to read their signals, or it can be used to stimulate them.
This Utah electrode array is being put into commercial products to help blind
people see, deaf people hear, and people who have lost the use of their limbs
to be able to regain that use or to be able to use bionic limbs as a substitute.
Very, very interesting research going on right now.
Now let's talk about power.
Power is given in watts, that is voltage times current.
So watts is volts times amps, so p is equal to VI.
Power is also the time rate of change of energy.
DW is not watts.
DW is energy, as the change of energy per time, and
that would be the power as a function of time.
The passive sign convention tells us if a device is consuming power or
producing power.
Here's how the passive sign convention works.
Define a device, shown here as the dark blue box, and one side of the device is a,
the other side is b.
Vab is the potential across that device, might be positive, might be negative.
Then define the current going into the device in the direction shown here,
from plus to minus.
The current is always defined as positive in this way.
Here's an example.
Here's the battery with a resistor.
I've chosen a single resistor here just for your simplicity.
The current, and we calculated this in Multisim before, is the voltage divided by
the resistance, or 1.5 milliamps in this case if we have a 1.5 volt battery.
Now, let's look over here and
determine what the voltage across that resistor is going to be.
The voltage is going to be IR.
I is 1.5 milliamps, the resistance is 1 kiloohms,
so the voltage across that resistor is 1.5 volts.
Now, let's see what happens with the power.
Let's first calculate the power here on the right, for the resistor.
Well, here's our device, this resistor, and
the voltage across it is 1.5 volts, positive 1.5 volts.
And the current is positive 1.5 milliamps.
So the power is going to be 1.5 volts times 1.5 milliamps or 2.25 milliwatts.
Since the power is positive, the resistor is consuming power.
That is what we expect.
In fact, resistors consume power and convert it into heat or light energy.
Now, let's come over to this side.
We know intrinsically that the battery must be producing power.
Let's see if that happens mathematically.
When we're looking at this, we're going to consider this to be our device, and
the current is coming into the device in the positive to negative direction.
The current, in this way, is 1.5 milliamps positive.
The voltage, if we're looking at it in this direction, from bottom to top, not
from top to bottom, from bottom to top, the voltage is going to be -1.5 volts.
So the power is equal to -1.5 volts times +1.5 milliamps for
a total of -2.25 milliwatts.
Remember, if the power is negative,
that means that the device is producing power instead of using power.
Another important feature of powers, the power has to be conserved within a system.
There's no place for loose power to be hanging out.
So we can see that our power that's produced is -2.25 milliwatts, the power
that is used is 2.25 milliwatts, and these two things have to be equal and opposite.
Now, let's talk about the energy.
The energy and the picture that we use for
that is W, the variable we use is W, that's given in Joules or kilowatt hours.
Most of the things that we use to measure in electrical engineering are kilowatt
hours, but
most of the things mechanical engineers will be talking about will be joules.
They are the same thing.
The energy is the integration over time of the power.
That means that we take the power, and all the power that we might have used all day,
if t is our day, is going to tell us how much energy we used.
1 joule is equal to 1 watt second, so
let's see what 1 kilowatt hour is equal to.
1 kilowatt hour, and let's balance our units, I need a watt on the bottom and
an hour on the bottom in order to cancel these out.
1 kilowatt hour times 1 joule per watt seconds,
times 60 seconds per minute, 60 minutes per hour.
My minutes cancel out, my seconds cancel out.
My watt hours cancel out, leaving me with Joules and this k over here, so
I get 3600 kilojoules.
1 kWh is 3600 kilojoules.
Now, let's figure out what energy you need, how much energy do you need?
This is a picture of the Internet base station on the mountain above my house.
It's a solar-powered base station.
The power is stored in car batteries, 12 volt batteries.
And then the base station, that's the little antenna right there,
is a line of site base station over the Park City for
mountain peak to mountain peak several miles away.
In order to figure out how much solar panel you need,
you first are going to make your device as efficient as possible.
Figure out how many kilowatts you need.
Then you're gong to decide how many hours that needs to be able to run.
Now, when you're considering the number of hours,
you want to consider how much time you can actually charge your solar panels,
which obviously is only during the day, and a fact that it's only the good days.
So if you have dark rainy days, you need to have enough power stored up.
So you take the number of hours, you multiply the number of appliances in
kilowatts times the number of hours you plan to use those devices, and
add it up to get kilowatt hours.
Consider the recharge time for night, dark or snowy days, etc.
I put some interesting links online so that you could calculate this for
an application of your interest, or
perhaps figure out just how much power you're using in your own home.
So our summary of voltage and power is we talked about what is voltage and
how you measure it.
It's polarity, the impact of using a ground and where you place the ground, and
what is power, and what is energy.
Then we talked about some interesting real applications.
Now, here is, you've wondered what is on the front side.
Here's the Solar Powered Neighborhood Internet Base Station
at the top of Emigration Canyon.
The view from above, over to Park City, you can see the mountain top that
it's transmitting to and receiving from is quite a distance away.
How do you get all that stuff up there, and
why do you care about the number of solar panels and the batteries?
Well, it's 200 pounds of car batteries carried up by people and by horses.
As well as the base station that you can see right here,
a couple of the neighbors carrying that up on a pole.
If you have to carry all of this stuff to the top of the mountain,
you are going to carry as few solar panels and as few batteries as possible.
So now, take a look at your own applications, find something interesting,
and estimate the amount of solar power that you would need for that application.