Welcome to the introduction to electrical and
computer engineering at the University of Utah.
I am Dr. Cynthia Furse, a professor of electrical and computer engineering.
Today we're going to be talking about units and scientific notation.
We're going to review the units that we'll be using throughout the semester.
We'll also review scientific notation, and
talk about converting between units in scientific notation.
The reason this is important is because electrical engineers use very large and
very small numbers all the time,
meaning that we need several different types of units.
I've chosen an example here of a company that's selling capacitors.
You can see that they're giving the capacitance in picofarads.
The voltage ratings are in volts and kilovolts.
The tolerance is either in percent or picofarad,
and the temperature coefficient amounting type are used.
So if you are searching for
a capacitors day, these are the units that you would have used.
We're going to use the international system of units in this class,
the SI units.
You'll remember these of course from physics, or from your previous experience.
The units of length is meters, mass, kilograms, time,
seconds, temperature, kelvin, voltage is a volt, and
here's the symbol that we're going to be using for that.
Current is given in amperes.
Here's the symbol that we'll be using for current.
Charge is coulombs.
Resistance is ohms and here's the symbol we'll be using for resistance.
Capacitance is farads and here's the symbol for capacitors.
Inductance is henrys, power is watts, frequency is hertz.
I've also given you the relationship between the various SI units for
our electrical components.
When we talk about very large, or very small numbers, we use special prefixes.
You've seen these before.
Prefixes that are very common in electrical engineering.
For example, if we were talking about frequency of wireless communication units,
would be giga, hertz, or megahertz, 10 to the 9 hertz, or 10 to the 6th.
Kilovolts, for example, 10 to the 3rd will be a large voltage.
If we were talking about numbers that are very small,
10 to the -3 to 10 to the -18 for example, we would be using these prefixes.
For example, capacitors are commonly sold in pico or nanofarad or
sometimes microfarad.
We'll commonly find inductors in microhenrys or millihenrys.
Milli is 10 to the minus 3rd, micro, 10 to the minus 6, nano,
10 to the minus 9th and so on.
There are several naming conventions that are used in our textbook and others.
Current is given as i, and voltage as v.
Whether they're straight or italicized, these may or may not be time varying,
they're just general used letters.
Time varying constants, current and voltage,
have this parentheses t, indicating that they are functions of time.
They are not constant.
Values that are constants are DC or direct current.
They are capitalized I and V shown here.
Bold letters aren't something special.
In our book, these are typically matrices, vectors, phasors, Laplace or
Fourier transforms.
When we want to convert from units to scientific notation,
what we do is we take the unit that we want such as milli,
and we just multiply the value by the number that goes with milli.
So for example, 1 MV is 1 times 10 to the -3 volt.
1 MV is 1 times 10 to the 6 volt.
If we want to convert from scientific notation back to units, what we do is
we take our scientific notation value, let's say 1 times 10 to the 6th, and
then we divide by the value associated with the unit we want.
Mega, for example, is 10 to the 6th, so we divide by 10 to the 6.
1 times 10 to the 6 is going to give us one megavolt.
Let's do this from millivolt.
1 times 10 to the -3 volt, divided by the 10 to the -3.
Which is associated with a millivolt.
And that's going to give us 1 millivolt.
If we want to convert from one unit to another, let say from millivolt to
microvolt, sometimes you can just see how to do this, that's fine.
But I'm also going to show you an easy way to do this with just to match the units.
We're going to use this throughout the semester periodically
when we have calculations to do.
Let's say, for example, we want to know how many microvolts are in one millivolt.
So here's question mark, how many microvolts, and here's the 1 millivolt.
Well, what we need to do is match units from this microvolt,
which we have to this millivolt that we want.
So, microvolt is 10 to the -6 volt.
Are we there yet?
Nope, we haven't gotten our millivolt taken care of.
Let's say now, we want to get rid of the volts and we want millivolts instead.
So, we're gonna say 10 to the minus 3rd volt per millivolt.
One millivolt is 10 to the minus 3rd volt.
And then we're gonna multiply this by 1 millivolt.
Now look what would happen.
We would be able to cancel out the volts.
We'd be able to cancel out the millivolts.
And we'd be left just with microvolts.
Hey, that's what we wanted.
The math here would be 10 to the -6 on the bottom, 10 to the minus 3rd on the top.
That gives us a value of 10 to the minus 3rd microvolts.
1 millivolt is indeed 10 to the 3rd microvolts.
Another way to do this is you can start with what you have.
We have 1 millivolt and we want to know how many microvolts.
So we take 1 millivolt.
We know that a millivolt, 1 millivolt is 10 to minus 3rd volt.
So here's how we can convert millivolts to volts.
Nope, that's not we wanted.
We wanted to get to microvolt.
Now let's convert volts to microvolts.
1 microvolt is 10 to the -6 volts.
Are volts we cancel out, are millivolts we cancel out,
leaving us with 10 to the 3rd microvolt.
So in conclusion, we've reviewed the units that we'll be using.
We've reviewed scientific notation and
we've talked about how to convert from one unit to another.
Throughout the semester, I'm going to include a picture on each of our lectures
of some of the beautiful places in the Great State of Utah.
This is Delicate Arch in Arches National Park.
Near Kanab, Utah, clearly one of the signature pictures from the state of Utah.