ECE 1250 Lecture for Chapter (1-2) Units & Scientific Notation

ECE 1250 Introduction to Electrical and Computer Engineering at the University of Utah. Class website: www.ece.utah.edu/~ece1250 This lecture reviews SI Units and Scientific Notation. By Dr. Cynthia Furse www.ece.utah.edu/~cfurse

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.