0:00:02.390,0:00:04.370 Welcome to Introduction to Electrical and 0:00:04.370,0:00:06.486 Computer Engineering at[br]the University of Utah. 0:00:06.486,0:00:11.530 I am Dr. Cynthia Furse, and today,[br]we'll be talking about voltage and power. 0:00:11.530,0:00:14.480 If you have ever wanted[br]to live off the grid, or 0:00:14.480,0:00:18.560 if you need an internet base station in[br]a remote area, or perhaps you just want to 0:00:18.560,0:00:22.090 be able to charge up the batteries[br]on your RV, this lecture is for you. 0:00:23.550,0:00:25.460 We're going to talk about what is voltage, 0:00:25.460,0:00:28.940 how do you measure it,[br]what's the polarity, ground, what's power, 0:00:28.940,0:00:32.220 what's energy, and then let's get real[br]with some interesting applications. 0:00:33.470,0:00:36.960 Voltage is the energy that's required[br]to move one unit of negative charge, 0:00:36.960,0:00:40.290 e minus, to point a to point b. 0:00:40.290,0:00:44.120 Another way to think of this is it's[br]the same energy that's required to lift 0:00:44.120,0:00:48.290 one unit of positive charge[br]e from point b to point a. 0:00:48.290,0:00:50.020 That's the way I like to think about it. 0:00:50.020,0:00:51.960 Voltage is equal to potential. 0:00:51.960,0:00:54.750 Think of the voltage as[br]a stack of positive charges 0:00:54.750,0:00:56.650 at the top of a hill at point a. 0:00:56.650,0:00:58.080 This has potential energy. 0:00:59.660,0:01:03.090 Voltages are potential differences[br]measured between two points. 0:01:03.090,0:01:07.710 You can see the voltmeter here who we've[br]connected the positive red lead onto a and 0:01:07.710,0:01:11.600 the common or negative ground lead onto b. 0:01:11.600,0:01:17.380 V from point a to point b, or[br]Vab, this include the 1.5 volts. 0:01:17.380,0:01:20.630 That means that Va is 1.5[br]volts higher than Vb. 0:01:23.160,0:01:24.460 Voltage has polarity. 0:01:24.460,0:01:26.050 What if I switch my leads? 0:01:26.050,0:01:30.570 What if I measure with a red lead at[br]point b and a negative lead at point a? 0:01:30.570,0:01:35.220 Then Vba will be read on[br]the volt meter as -1.5 volts. 0:01:35.220,0:01:39.800 That means that Vb is[br]1.5 volts lower than Va. 0:01:39.800,0:01:44.240 You could stop for a minute, if you like,[br]and use Multisim to be able to experiment 0:01:44.240,0:01:47.590 with your voltage and your voltmeter[br]to be able to see this happen. 0:01:49.590,0:01:52.130 Voltage is always measured[br]relative to a ground. 0:01:52.130,0:01:54.680 We also call that the reference or[br]the neutral. 0:01:54.680,0:01:58.950 Here are two cards that show you what[br]symbols we might use for ground. 0:01:58.950,0:02:02.200 We always define the voltage of[br]the ground as being 0 volts. 0:02:04.100,0:02:06.540 Here's an example of[br]a very simple circuit. 0:02:06.540,0:02:07.600 This is where we have a battery. 0:02:07.600,0:02:09.840 It's connected onto two resistors. 0:02:09.840,0:02:15.160 And we might be interested in knowing,[br]what is Vc in-between these two resistors? 0:02:15.160,0:02:18.980 Well, we can tell one thing[br]about this particular picture. 0:02:18.980,0:02:24.000 We know that Vab is 1.5 volts[br]because I bought a 1.5 volt battery. 0:02:24.000,0:02:28.140 But without having a ground,[br]I can't tell you exactly what Vc is. 0:02:28.140,0:02:32.110 So let's define the ground at[br]a place that's convenient to us. 0:02:32.110,0:02:35.571 For me, the most convenient place[br]is at the bottom of the battery, so 0:02:35.571,0:02:38.451 I'm going to install my ground[br]right here at this point. 0:02:38.451,0:02:42.573 Then I can say, what's Va,[br]what's Vb, and what's Vc? 0:02:42.573,0:02:45.326 Let's start with Vb, that's the easiest. 0:02:45.326,0:02:46.488 Okay, check this out. 0:02:46.488,0:02:52.050 Vb is directly connected onto the ground,[br]so I know that Vb is 0 volts. 0:02:52.050,0:02:53.700 That's my definition. 0:02:53.700,0:02:57.100 I'm gonna use three lines to[br]say Vb is defined as zero 0:02:57.100,0:02:59.170 because that's where I put my ground. 0:02:59.170,0:03:00.710 Now, what about Va? 0:03:00.710,0:03:06.136 Remember that Va is 1.5 volts above Vb, 0:03:06.136,0:03:10.516 Vb is zero, so Va is 1.5 volts. 0:03:10.516,0:03:12.354 Now, what about Vc? 0:03:12.354,0:03:15.380 We can see that these[br]two resistors are equal. 0:03:15.380,0:03:18.970 That means that the voltage is going[br]to be evenly split between them. 0:03:18.970,0:03:24.910 The voltage between this point right here[br]and the bottom, which is 0, is 1.5 volts. 0:03:24.910,0:03:29.230 So Vc is going to be halfway[br]in between 1.5 volts and 0, 0:03:29.230,0:03:33.161 where it's going to be 0.75 volts. 0:03:35.200,0:03:38.310 Now, this particular definition of Va,[br]Vb, and 0:03:38.310,0:03:42.000 Vc is totally dependent on[br]where I placed my ground. 0:03:42.000,0:03:43.985 Let me show you what I mean. 0:03:43.985,0:03:45.800 Let's go choose a different ground point. 0:03:47.360,0:03:51.190 This time, let's put our ground right[br]here in-between the two resistors. 0:03:51.190,0:03:53.240 It's legal, we can go ahead and do that. 0:03:53.240,0:03:56.260 It may not be quite as convenient,[br]but let's see what happens. 0:03:56.260,0:03:58.410 Okay, Vc is at the point of the ground. 0:03:58.410,0:04:04.711 So remember, the ground defines our[br]voltage as being 0, so Vc is equal to 0. 0:04:04.711,0:04:07.507 Now, what about Va and Vb? 0:04:07.507,0:04:11.576 Well, we know that Va is[br]1.5 volts higher than Vb. 0:04:11.576,0:04:14.674 And how about its relationship to Vc? 0:04:14.674,0:04:18.861 Well, because we originally[br]split the voltage here, 0:04:18.861,0:04:23.867 we're going to still be splitting[br]the voltage, so we can see that 0:04:23.867,0:04:30.258 Va is going to be 0.75 volts higher than[br]Vc, so Va is going to be 0.75 volts. 0:04:30.258,0:04:32.133 All right, what about Vb? 0:04:32.133,0:04:37.226 Well, that's going to be[br]0.75 volts lower than Vc, 0:04:37.226,0:04:40.963 so that's going to be -0.75 volts. 0:04:40.963,0:04:43.869 Let's kinda check ourselves. 0:04:43.869,0:04:48.323 We know that Vab has to be 1.5 volts,[br]is that going to be true? 0:04:48.323,0:04:53.141 Va is 0.75 volts, Vb is -0.75 volts, so 0:04:53.141,0:04:57.520 absolutely, we got our 1.5 volts. 0:04:57.520,0:05:01.100 Now, notice that the relative voltages in[br]this circuit are the same as they were 0:05:01.100,0:05:03.700 before when we had our[br]ground at the bottom, but 0:05:03.700,0:05:07.180 the absolute values of these[br]voltages are different. 0:05:07.180,0:05:08.290 Does it matter? 0:05:08.290,0:05:09.970 The answer is no. 0:05:09.970,0:05:14.520 Everything in my circuit can be relative[br]to the ground at any location, and 0:05:14.520,0:05:16.810 I can do my calculations accordingly. 0:05:16.810,0:05:19.490 So it doesn't matter where I put my ground 0:05:19.490,0:05:23.700 except that I'm most often going to[br]choose it for my calculation convenience. 0:05:24.980,0:05:26.550 Okay, let's go on to the next idea. 0:05:28.100,0:05:29.940 Let's talk about some real stuff. 0:05:29.940,0:05:33.290 So what's a really big voltage, and[br]what's a really little voltage? 0:05:33.290,0:05:36.580 Let's have some ideas in mind so[br]that when we do our calculations, 0:05:36.580,0:05:40.690 our math, we have an idea if we're[br]getting something that's reasonable. 0:05:40.690,0:05:43.746 The biggest voltage that I could[br]find in nature is lightning. 0:05:43.746,0:05:46.926 It's not uncommon for[br]lightning to have 1 billion volts. 0:05:46.926,0:05:50.774 That's one times tenth to the ninth,[br]that is really big voltage. 0:05:50.774,0:05:54.282 There's some interesting information on[br]lightning in the reference material at 0:05:54.282,0:05:56.340 the end of this lecture. 0:05:56.340,0:05:59.050 High voltage lines also[br]have large voltage. 0:05:59.050,0:06:02.750 High voltage lines are often 110[br]kilovolts or higher, and indeed, 0:06:02.750,0:06:05.310 they are considered high voltage. 0:06:05.310,0:06:09.528 Your house, your residential[br]construction has 240 volts for 0:06:09.528,0:06:13.753 your largest appliances and[br]120 for most of your general use. 0:06:15.255,0:06:17.550 Now, what's a really small voltage? 0:06:17.550,0:06:22.110 Neural action potentials, the electric[br]potential that stimulates a single neuron, 0:06:22.110,0:06:23.990 is a relatively small voltage. 0:06:23.990,0:06:26.670 That's about -55 millivolts. 0:06:26.670,0:06:33.840 Your cardiac action potential is about the[br]same range, that's -100 to +50 millivolts. 0:06:33.840,0:06:37.810 A bird sitting on a power line is[br]another example of a very small voltage. 0:06:37.810,0:06:40.390 We say the bird can sit on[br]the line without being shocked 0:06:40.390,0:06:42.540 because it has no potential difference. 0:06:42.540,0:06:43.810 It's not exactly right. 0:06:43.810,0:06:47.809 Has a very small potential difference of[br]about 10 millivolts between the left and 0:06:47.809,0:06:51.252 the right leg, and that is small[br]enough that it doesn't hurt the bird. 0:06:52.517,0:06:56.381 There's some very interesting research[br]going on at the University of Utah 0:06:56.381,0:07:00.950 relative to electrodes and neurons[br]that you might be very interested in. 0:07:00.950,0:07:06.050 The Utah electrode array is a very small[br]array made from silicone that has ten 0:07:06.050,0:07:07.950 electrodes by ten electrodes. 0:07:07.950,0:07:09.560 Each electrode is like a tiny needle. 0:07:09.560,0:07:14.550 It's made from silicon, it is conductive,[br]it's connected to an individual line. 0:07:14.550,0:07:19.050 If you look at this big kind of gold line[br]right here, that has 100 little different 0:07:19.050,0:07:23.650 lines, about [INAUDIBLE] of hair[br]that come back to a central system. 0:07:23.650,0:07:28.370 This electrode array can be placed in or[br]in contact with any nerve. 0:07:28.370,0:07:32.000 For example, it could be stuck[br]on the surface of the brain. 0:07:32.000,0:07:34.430 This can be used to either[br]receive from the nerves and 0:07:34.430,0:07:38.310 be able to read their signals, or[br]it can be used to stimulate them. 0:07:38.310,0:07:42.420 This Utah electrode array is being put[br]into commercial products to help blind 0:07:42.420,0:07:47.450 people see, deaf people hear, and people[br]who have lost the use of their limbs 0:07:47.450,0:07:53.120 to be able to regain that use or to be[br]able to use bionic limbs as a substitute. 0:07:53.120,0:07:55.250 Very, very interesting[br]research going on right now. 0:07:56.960,0:07:58.690 Now let's talk about power. 0:07:58.690,0:08:02.100 Power is given in watts,[br]that is voltage times current. 0:08:02.100,0:08:07.120 So watts is volts times amps,[br]so p is equal to VI. 0:08:07.120,0:08:10.189 Power is also the time[br]rate of change of energy. 0:08:10.189,0:08:11.894 DW is not watts. 0:08:11.894,0:08:14.907 DW is energy,[br]as the change of energy per time, and 0:08:14.907,0:08:17.580 that would be the power[br]as a function of time. 0:08:19.380,0:08:23.160 The passive sign convention tells us[br]if a device is consuming power or 0:08:23.160,0:08:24.500 producing power. 0:08:24.500,0:08:27.028 Here's how the passive[br]sign convention works. 0:08:27.028,0:08:32.009 Define a device, shown here as the dark[br]blue box, and one side of the device is a, 0:08:32.009,0:08:33.270 the other side is b. 0:08:33.270,0:08:39.150 Vab is the potential across that device,[br]might be positive, might be negative. 0:08:39.150,0:08:42.780 Then define the current going into[br]the device in the direction shown here, 0:08:42.780,0:08:44.390 from plus to minus. 0:08:44.390,0:08:46.785 The current is always defined[br]as positive in this way. 0:08:48.850,0:08:50.460 Here's an example. 0:08:50.460,0:08:52.010 Here's the battery with a resistor. 0:08:52.010,0:08:55.510 I've chosen a single resistor[br]here just for your simplicity. 0:08:55.510,0:09:00.100 The current, and we calculated this in[br]Multisim before, is the voltage divided by 0:09:00.100,0:09:05.920 the resistance, or 1.5 milliamps in[br]this case if we have a 1.5 volt battery. 0:09:05.920,0:09:07.500 Now, let's look over here and 0:09:07.500,0:09:10.720 determine what the voltage across[br]that resistor is going to be. 0:09:10.720,0:09:12.790 The voltage is going to be IR. 0:09:12.790,0:09:16.055 I is 1.5 milliamps,[br]the resistance is 1 kiloohms, 0:09:16.055,0:09:19.184 so the voltage across that[br]resistor is 1.5 volts. 0:09:20.310,0:09:22.550 Now, let's see what[br]happens with the power. 0:09:22.550,0:09:26.060 Let's first calculate the power here[br]on the right, for the resistor. 0:09:26.060,0:09:29.780 Well, here's our device,[br]this resistor, and 0:09:29.780,0:09:33.920 the voltage across it is 1.5 volts,[br]positive 1.5 volts. 0:09:33.920,0:09:37.700 And the current is positive 1.5 milliamps. 0:09:37.700,0:09:44.430 So the power is going to be 1.5 volts[br]times 1.5 milliamps or 2.25 milliwatts. 0:09:44.430,0:09:48.100 Since the power is positive,[br]the resistor is consuming power. 0:09:48.100,0:09:49.020 That is what we expect. 0:09:49.020,0:09:54.510 In fact, resistors consume power and[br]convert it into heat or light energy. 0:09:54.510,0:09:56.290 Now, let's come over to this side. 0:09:56.290,0:09:59.523 We know intrinsically that[br]the battery must be producing power. 0:09:59.523,0:10:02.006 Let's see if that happens mathematically. 0:10:02.006,0:10:06.086 When we're looking at this, we're going[br]to consider this to be our device, and 0:10:06.086,0:10:10.450 the current is coming into the device[br]in the positive to negative direction. 0:10:10.450,0:10:14.020 The current, in this way,[br]is 1.5 milliamps positive. 0:10:14.020,0:10:18.510 The voltage, if we're looking at it in[br]this direction, from bottom to top, not 0:10:18.510,0:10:24.200 from top to bottom, from bottom to top,[br]the voltage is going to be -1.5 volts. 0:10:24.200,0:10:29.390 So the power is equal to -1.5[br]volts times +1.5 milliamps for 0:10:29.390,0:10:32.580 a total of -2.25 milliwatts. 0:10:32.580,0:10:34.440 Remember, if the power is negative, 0:10:34.440,0:10:38.780 that means that the device is producing[br]power instead of using power. 0:10:38.780,0:10:43.520 Another important feature of powers, the[br]power has to be conserved within a system. 0:10:43.520,0:10:46.460 There's no place for[br]loose power to be hanging out. 0:10:46.460,0:10:51.298 So we can see that our power that's[br]produced is -2.25 milliwatts, the power 0:10:51.298,0:10:56.571 that is used is 2.25 milliwatts, and these[br]two things have to be equal and opposite. 0:10:58.536,0:11:00.630 Now, let's talk about the energy. 0:11:00.630,0:11:04.070 The energy and the picture that we use for 0:11:04.070,0:11:09.330 that is W, the variable we use is W,[br]that's given in Joules or kilowatt hours. 0:11:09.330,0:11:12.818 Most of the things that we use to measure[br]in electrical engineering are kilowatt 0:11:12.818,0:11:13.338 hours, but 0:11:13.338,0:11:16.788 most of the things mechanical engineers[br]will be talking about will be joules. 0:11:16.788,0:11:24.001 They are the same thing. 0:11:24.001,0:11:27.777 The energy is the integration[br]over time of the power. 0:11:27.777,0:11:32.277 That means that we take the power, and all[br]the power that we might have used all day, 0:11:32.277,0:11:35.450 if t is our day, is going to[br]tell us how much energy we used. 0:11:35.450,0:11:38.900 1 joule is equal to 1 watt second, so 0:11:38.900,0:11:42.145 let's see what 1 kilowatt[br]hour is equal to. 0:11:42.145,0:11:47.010 1 kilowatt hour, and let's balance our[br]units, I need a watt on the bottom and 0:11:47.010,0:11:49.785 an hour on the bottom in[br]order to cancel these out. 0:11:49.785,0:11:52.704 1 kilowatt hour times 1[br]joule per watt seconds, 0:11:52.704,0:11:56.320 times 60 seconds per minute,[br]60 minutes per hour. 0:11:56.320,0:11:59.199 My minutes cancel out,[br]my seconds cancel out. 0:11:59.199,0:12:04.109 My watt hours cancel out, leaving me[br]with Joules and this k over here, so 0:12:04.109,0:12:06.052 I get 3600 kilojoules. 0:12:06.052,0:12:09.703 1 kWh is 3600 kilojoules. 0:12:11.230,0:12:16.180 Now, let's figure out what energy you[br]need, how much energy do you need? 0:12:16.180,0:12:20.110 This is a picture of the Internet base[br]station on the mountain above my house. 0:12:20.110,0:12:21.840 It's a solar-powered base station. 0:12:21.840,0:12:25.140 The power is stored in car batteries,[br]12 volt batteries. 0:12:25.140,0:12:28.080 And then the base station,[br]that's the little antenna right there, 0:12:28.080,0:12:30.750 is a line of site base station[br]over the Park City for 0:12:30.750,0:12:34.120 mountain peak to mountain[br]peak several miles away. 0:12:34.120,0:12:37.180 In order to figure out how[br]much solar panel you need, 0:12:37.180,0:12:40.440 you first are going to make your[br]device as efficient as possible. 0:12:40.440,0:12:42.365 Figure out how many kilowatts you need. 0:12:42.365,0:12:45.971 Then you're gong to decide how many[br]hours that needs to be able to run. 0:12:45.971,0:12:48.435 Now, when you're considering[br]the number of hours, 0:12:48.435,0:12:51.995 you want to consider how much time you[br]can actually charge your solar panels, 0:12:51.995,0:12:56.160 which obviously is only during the day,[br]and a fact that it's only the good days. 0:12:56.160,0:12:59.890 So if you have dark rainy days,[br]you need to have enough power stored up. 0:12:59.890,0:13:04.320 So you take the number of hours,[br]you multiply the number of appliances in 0:13:04.320,0:13:08.980 kilowatts times the number of hours[br]you plan to use those devices, and 0:13:08.980,0:13:11.250 add it up to get kilowatt hours. 0:13:11.250,0:13:16.480 Consider the recharge time for[br]night, dark or snowy days, etc. 0:13:16.480,0:13:19.470 I put some interesting links online so[br]that you could calculate this for 0:13:19.470,0:13:21.690 an application of your interest, or 0:13:21.690,0:13:24.950 perhaps figure out just how much[br]power you're using in your own home. 0:13:26.830,0:13:30.630 So our summary of voltage and power is[br]we talked about what is voltage and 0:13:30.630,0:13:31.940 how you measure it. 0:13:31.940,0:13:36.450 It's polarity, the impact of using a[br]ground and where you place the ground, and 0:13:36.450,0:13:38.620 what is power, and what is energy. 0:13:38.620,0:13:41.109 Then we talked about some[br]interesting real applications. 0:13:42.270,0:13:45.115 Now, here is,[br]you've wondered what is on the front side. 0:13:45.115,0:13:47.930 Here's the Solar Powered[br]Neighborhood Internet Base Station 0:13:47.930,0:13:49.390 at the top of Emigration Canyon. 0:13:50.520,0:13:54.486 The view from above, over to Park City,[br]you can see the mountain top that 0:13:54.486,0:13:58.209 it's transmitting to and[br]receiving from is quite a distance away. 0:13:58.209,0:14:00.239 How do you get all that stuff up there,[br]and 0:14:00.239,0:14:03.496 why do you care about the number[br]of solar panels and the batteries? 0:14:03.496,0:14:08.730 Well, it's 200 pounds of car batteries[br]carried up by people and by horses. 0:14:08.730,0:14:11.010 As well as the base station[br]that you can see right here, 0:14:11.010,0:14:14.070 a couple of the neighbors[br]carrying that up on a pole. 0:14:14.070,0:14:16.061 If you have to carry all of this[br]stuff to the top of the mountain, 0:14:16.061,0:14:20.190 you are going to carry as few solar[br]panels and as few batteries as possible. 0:14:21.270,0:14:24.930 So now, take a look at your own[br]applications, find something interesting, 0:14:24.930,0:14:29.090 and estimate the amount of solar power[br]that you would need for that application.