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Welcome to the introduction[br]to electrical and

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computer engineering at[br]the University of Utah.

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I am Dr. Cynthia Furse, a professor of[br]electrical and computer engineering.

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Today we're going to be talking[br]about units and scientific notation.

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We're going to review the units that[br]we'll be using throughout the semester.

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We'll also review scientific notation, and

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talk about converting between[br]units in scientific notation.

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The reason this is important is because[br]electrical engineers use very large and

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very small numbers all the time,

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meaning that we need several[br]different types of units.

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I've chosen an example here of[br]a company that's selling capacitors.

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You can see that they're giving[br]the capacitance in picofarads.

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The voltage ratings are in volts and[br]kilovolts.

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The tolerance is either in percent or[br]picofarad,

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and the temperature coefficient[br]amounting type are used.

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So if you are searching for

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a capacitors day, these are the units[br]that you would have used.

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We're going to use the international[br]system of units in this class,

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the SI units.

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You'll remember these of course from[br]physics, or from your previous experience.

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The units of length is meters,[br]mass, kilograms, time,

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seconds, temperature, kelvin,[br]voltage is a volt, and

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here's the symbol that we're[br]going to be using for that.

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Current is given in amperes.

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Here's the symbol that we'll be using for[br]current.

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Charge is coulombs.

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Resistance is ohms and here's the symbol[br]we'll be using for resistance.

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Capacitance is farads and[br]here's the symbol for capacitors.

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Inductance is henrys,[br]power is watts, frequency is hertz.

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I've also given you the relationship[br]between the various SI units for

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our electrical components.

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When we talk about very large, or very[br]small numbers, we use special prefixes.

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You've seen these before.

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Prefixes that are very common[br]in electrical engineering.

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For example, if we were talking about[br]frequency of wireless communication units,

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would be giga, hertz, or megahertz,[br]10 to the 9 hertz, or 10 to the 6th.

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Kilovolts, for example,[br]10 to the 3rd will be a large voltage.

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If we were talking about[br]numbers that are very small,

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10 to the -3 to 10 to the -18 for example,[br]we would be using these prefixes.

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For example, capacitors are commonly[br]sold in pico or nanofarad or

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sometimes microfarad.

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We'll commonly find inductors[br]in microhenrys or millihenrys.

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Milli is 10 to the minus 3rd,[br]micro, 10 to the minus 6, nano,

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10 to the minus 9th and so on.

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There are several naming conventions that[br]are used in our textbook and others.

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Current is given as i, and voltage as v.

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Whether they're straight or italicized,[br]these may or may not be time varying,

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they're just general used letters.

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Time varying constants,[br]current and voltage,

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have this parentheses t, indicating[br]that they are functions of time.

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They are not constant.

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Values that are constants are DC or[br]direct current.

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They are capitalized I and V shown here.

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Bold letters aren't something special.

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In our book, these are typically matrices,[br]vectors, phasors, Laplace or

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Fourier transforms.

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When we want to convert from[br]units to scientific notation,

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what we do is we take the unit[br]that we want such as milli,

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and we just multiply the value by[br]the number that goes with milli.

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So for example,[br]1 MV is 1 times 10 to the -3 volt.

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1 MV is 1 times 10 to the 6 volt.

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If we want to convert from scientific[br]notation back to units, what we do is

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we take our scientific notation value,[br]let's say 1 times 10 to the 6th, and

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then we divide by the value[br]associated with the unit we want.

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Mega, for example, is 10 to the 6th,[br]so we divide by 10 to the 6.

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1 times 10 to the 6 is going[br]to give us one megavolt.

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Let's do this from millivolt.

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1 times 10 to the -3 volt,[br]divided by the 10 to the -3.

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Which is associated with a millivolt.

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And that's going to give us 1 millivolt.

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If we want to convert from one unit[br]to another, let say from millivolt to

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microvolt, sometimes you can just[br]see how to do this, that's fine.

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But I'm also going to show you an easy way[br]to do this with just to match the units.

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We're going to use this throughout[br]the semester periodically

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when we have calculations to do.

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Let's say, for example, we want to know[br]how many microvolts are in one millivolt.

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So here's question mark, how many[br]microvolts, and here's the 1 millivolt.

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Well, what we need to do is[br]match units from this microvolt,

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which we have to this[br]millivolt that we want.

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So, microvolt is 10 to the -6 volt.

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Are we there yet?

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Nope, we haven't gotten our[br]millivolt taken care of.

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Let's say now, we want to get rid of[br]the volts and we want millivolts instead.

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So, we're gonna say 10 to[br]the minus 3rd volt per millivolt.

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One millivolt is 10 to the minus 3rd volt.

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And then we're gonna multiply[br]this by 1 millivolt.

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Now look what would happen.

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We would be able to cancel out the volts.

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We'd be able to cancel out the millivolts.

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And we'd be left just with microvolts.

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Hey, that's what we wanted.

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The math here would be 10 to the -6 on the[br]bottom, 10 to the minus 3rd on the top.

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That gives us a value of 10[br]to the minus 3rd microvolts.

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1 millivolt is indeed 10[br]to the 3rd microvolts.

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Another way to do this is you[br]can start with what you have.

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We have 1 millivolt and[br]we want to know how many microvolts.

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So we take 1 millivolt.

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We know that a millivolt,[br]1 millivolt is 10 to minus 3rd volt.

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So here's how we can convert[br]millivolts to volts.

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Nope, that's not we wanted.

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We wanted to get to microvolt.

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Now let's convert volts to microvolts.

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1 microvolt is 10 to the -6 volts.

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Are volts we cancel out,[br]are millivolts we cancel out,

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leaving us with 10 to the 3rd microvolt.

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So in conclusion, we've reviewed[br]the units that we'll be using.

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We've reviewed scientific notation and

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we've talked about how to convert[br]from one unit to another.

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Throughout the semester, I'm going to[br]include a picture on each of our lectures

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of some of the beautiful places[br]in the Great State of Utah.

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This is Delicate Arch in[br]Arches National Park.

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Near Kanab, Utah, clearly one of the[br]signature pictures from the state of Utah.