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.