1 00:00:02,390 --> 00:00:04,370 Welcome to Introduction to Electrical and 2 00:00:04,370 --> 00:00:06,486 Computer Engineering at the University of Utah. 3 00:00:06,486 --> 00:00:11,530 I am Dr. Cynthia Furse, and today, we'll be talking about voltage and power. 4 00:00:11,530 --> 00:00:14,480 If you have ever wanted to live off the grid, or 5 00:00:14,480 --> 00:00:18,560 if you need an internet base station in a remote area, or perhaps you just want to 6 00:00:18,560 --> 00:00:22,090 be able to charge up the batteries on your RV, this lecture is for you. 7 00:00:23,550 --> 00:00:25,460 We're going to talk about what is voltage, 8 00:00:25,460 --> 00:00:28,940 how do you measure it, what's the polarity, ground, what's power, 9 00:00:28,940 --> 00:00:32,220 what's energy, and then let's get real with some interesting applications. 10 00:00:33,470 --> 00:00:36,960 Voltage is the energy that's required to move one unit of negative charge, 11 00:00:36,960 --> 00:00:40,290 e minus, to point a to point b. 12 00:00:40,290 --> 00:00:44,120 Another way to think of this is it's the same energy that's required to lift 13 00:00:44,120 --> 00:00:48,290 one unit of positive charge e from point b to point a. 14 00:00:48,290 --> 00:00:50,020 That's the way I like to think about it. 15 00:00:50,020 --> 00:00:51,960 Voltage is equal to potential. 16 00:00:51,960 --> 00:00:54,750 Think of the voltage as a stack of positive charges 17 00:00:54,750 --> 00:00:56,650 at the top of a hill at point a. 18 00:00:56,650 --> 00:00:58,080 This has potential energy. 19 00:00:59,660 --> 00:01:03,090 Voltages are potential differences measured between two points. 20 00:01:03,090 --> 00:01:07,710 You can see the voltmeter here who we've connected the positive red lead onto a and 21 00:01:07,710 --> 00:01:11,600 the common or negative ground lead onto b. 22 00:01:11,600 --> 00:01:17,380 V from point a to point b, or Vab, this include the 1.5 volts. 23 00:01:17,380 --> 00:01:20,630 That means that Va is 1.5 volts higher than Vb. 24 00:01:23,160 --> 00:01:24,460 Voltage has polarity. 25 00:01:24,460 --> 00:01:26,050 What if I switch my leads? 26 00:01:26,050 --> 00:01:30,570 What if I measure with a red lead at point b and a negative lead at point a? 27 00:01:30,570 --> 00:01:35,220 Then Vba will be read on the volt meter as -1.5 volts. 28 00:01:35,220 --> 00:01:39,800 That means that Vb is 1.5 volts lower than Va. 29 00:01:39,800 --> 00:01:44,240 You could stop for a minute, if you like, and use Multisim to be able to experiment 30 00:01:44,240 --> 00:01:47,590 with your voltage and your voltmeter to be able to see this happen. 31 00:01:49,590 --> 00:01:52,130 Voltage is always measured relative to a ground. 32 00:01:52,130 --> 00:01:54,680 We also call that the reference or the neutral. 33 00:01:54,680 --> 00:01:58,950 Here are two cards that show you what symbols we might use for ground. 34 00:01:58,950 --> 00:02:02,200 We always define the voltage of the ground as being 0 volts. 35 00:02:04,100 --> 00:02:06,540 Here's an example of a very simple circuit. 36 00:02:06,540 --> 00:02:07,600 This is where we have a battery. 37 00:02:07,600 --> 00:02:09,840 It's connected onto two resistors. 38 00:02:09,840 --> 00:02:15,160 And we might be interested in knowing, what is Vc in-between these two resistors? 39 00:02:15,160 --> 00:02:18,980 Well, we can tell one thing about this particular picture. 40 00:02:18,980 --> 00:02:24,000 We know that Vab is 1.5 volts because I bought a 1.5 volt battery. 41 00:02:24,000 --> 00:02:28,140 But without having a ground, I can't tell you exactly what Vc is. 42 00:02:28,140 --> 00:02:32,110 So let's define the ground at a place that's convenient to us. 43 00:02:32,110 --> 00:02:35,571 For me, the most convenient place is at the bottom of the battery, so 44 00:02:35,571 --> 00:02:38,451 I'm going to install my ground right here at this point. 45 00:02:38,451 --> 00:02:42,573 Then I can say, what's Va, what's Vb, and what's Vc? 46 00:02:42,573 --> 00:02:45,326 Let's start with Vb, that's the easiest. 47 00:02:45,326 --> 00:02:46,488 Okay, check this out. 48 00:02:46,488 --> 00:02:52,050 Vb is directly connected onto the ground, so I know that Vb is 0 volts. 49 00:02:52,050 --> 00:02:53,700 That's my definition. 50 00:02:53,700 --> 00:02:57,100 I'm gonna use three lines to say Vb is defined as zero 51 00:02:57,100 --> 00:02:59,170 because that's where I put my ground. 52 00:02:59,170 --> 00:03:00,710 Now, what about Va? 53 00:03:00,710 --> 00:03:06,136 Remember that Va is 1.5 volts above Vb, 54 00:03:06,136 --> 00:03:10,516 Vb is zero, so Va is 1.5 volts. 55 00:03:10,516 --> 00:03:12,354 Now, what about Vc? 56 00:03:12,354 --> 00:03:15,380 We can see that these two resistors are equal. 57 00:03:15,380 --> 00:03:18,970 That means that the voltage is going to be evenly split between them. 58 00:03:18,970 --> 00:03:24,910 The voltage between this point right here and the bottom, which is 0, is 1.5 volts. 59 00:03:24,910 --> 00:03:29,230 So Vc is going to be halfway in between 1.5 volts and 0, 60 00:03:29,230 --> 00:03:33,161 where it's going to be 0.75 volts. 61 00:03:35,200 --> 00:03:38,310 Now, this particular definition of Va, Vb, and 62 00:03:38,310 --> 00:03:42,000 Vc is totally dependent on where I placed my ground. 63 00:03:42,000 --> 00:03:43,985 Let me show you what I mean. 64 00:03:43,985 --> 00:03:45,800 Let's go choose a different ground point. 65 00:03:47,360 --> 00:03:51,190 This time, let's put our ground right here in-between the two resistors. 66 00:03:51,190 --> 00:03:53,240 It's legal, we can go ahead and do that. 67 00:03:53,240 --> 00:03:56,260 It may not be quite as convenient, but let's see what happens. 68 00:03:56,260 --> 00:03:58,410 Okay, Vc is at the point of the ground. 69 00:03:58,410 --> 00:04:04,711 So remember, the ground defines our voltage as being 0, so Vc is equal to 0. 70 00:04:04,711 --> 00:04:07,507 Now, what about Va and Vb? 71 00:04:07,507 --> 00:04:11,576 Well, we know that Va is 1.5 volts higher than Vb. 72 00:04:11,576 --> 00:04:14,674 And how about its relationship to Vc? 73 00:04:14,674 --> 00:04:18,861 Well, because we originally split the voltage here, 74 00:04:18,861 --> 00:04:23,867 we're going to still be splitting the voltage, so we can see that 75 00:04:23,867 --> 00:04:30,258 Va is going to be 0.75 volts higher than Vc, so Va is going to be 0.75 volts. 76 00:04:30,258 --> 00:04:32,133 All right, what about Vb? 77 00:04:32,133 --> 00:04:37,226 Well, that's going to be 0.75 volts lower than Vc, 78 00:04:37,226 --> 00:04:40,963 so that's going to be -0.75 volts. 79 00:04:40,963 --> 00:04:43,869 Let's kinda check ourselves. 80 00:04:43,869 --> 00:04:48,323 We know that Vab has to be 1.5 volts, is that going to be true? 81 00:04:48,323 --> 00:04:53,141 Va is 0.75 volts, Vb is -0.75 volts, so 82 00:04:53,141 --> 00:04:57,520 absolutely, we got our 1.5 volts. 83 00:04:57,520 --> 00:05:01,100 Now, notice that the relative voltages in this circuit are the same as they were 84 00:05:01,100 --> 00:05:03,700 before when we had our ground at the bottom, but 85 00:05:03,700 --> 00:05:07,180 the absolute values of these voltages are different. 86 00:05:07,180 --> 00:05:08,290 Does it matter? 87 00:05:08,290 --> 00:05:09,970 The answer is no. 88 00:05:09,970 --> 00:05:14,520 Everything in my circuit can be relative to the ground at any location, and 89 00:05:14,520 --> 00:05:16,810 I can do my calculations accordingly. 90 00:05:16,810 --> 00:05:19,490 So it doesn't matter where I put my ground 91 00:05:19,490 --> 00:05:23,700 except that I'm most often going to choose it for my calculation convenience. 92 00:05:24,980 --> 00:05:26,550 Okay, let's go on to the next idea. 93 00:05:28,100 --> 00:05:29,940 Let's talk about some real stuff. 94 00:05:29,940 --> 00:05:33,290 So what's a really big voltage, and what's a really little voltage? 95 00:05:33,290 --> 00:05:36,580 Let's have some ideas in mind so that when we do our calculations, 96 00:05:36,580 --> 00:05:40,690 our math, we have an idea if we're getting something that's reasonable. 97 00:05:40,690 --> 00:05:43,746 The biggest voltage that I could find in nature is lightning. 98 00:05:43,746 --> 00:05:46,926 It's not uncommon for lightning to have 1 billion volts. 99 00:05:46,926 --> 00:05:50,774 That's one times tenth to the ninth, that is really big voltage. 100 00:05:50,774 --> 00:05:54,282 There's some interesting information on lightning in the reference material at 101 00:05:54,282 --> 00:05:56,340 the end of this lecture. 102 00:05:56,340 --> 00:05:59,050 High voltage lines also have large voltage. 103 00:05:59,050 --> 00:06:02,750 High voltage lines are often 110 kilovolts or higher, and indeed, 104 00:06:02,750 --> 00:06:05,310 they are considered high voltage. 105 00:06:05,310 --> 00:06:09,528 Your house, your residential construction has 240 volts for 106 00:06:09,528 --> 00:06:13,753 your largest appliances and 120 for most of your general use. 107 00:06:15,255 --> 00:06:17,550 Now, what's a really small voltage? 108 00:06:17,550 --> 00:06:22,110 Neural action potentials, the electric potential that stimulates a single neuron, 109 00:06:22,110 --> 00:06:23,990 is a relatively small voltage. 110 00:06:23,990 --> 00:06:26,670 That's about -55 millivolts. 111 00:06:26,670 --> 00:06:33,840 Your cardiac action potential is about the same range, that's -100 to +50 millivolts. 112 00:06:33,840 --> 00:06:37,810 A bird sitting on a power line is another example of a very small voltage. 113 00:06:37,810 --> 00:06:40,390 We say the bird can sit on the line without being shocked 114 00:06:40,390 --> 00:06:42,540 because it has no potential difference. 115 00:06:42,540 --> 00:06:43,810 It's not exactly right. 116 00:06:43,810 --> 00:06:47,809 Has a very small potential difference of about 10 millivolts between the left and 117 00:06:47,809 --> 00:06:51,252 the right leg, and that is small enough that it doesn't hurt the bird. 118 00:06:52,517 --> 00:06:56,381 There's some very interesting research going on at the University of Utah 119 00:06:56,381 --> 00:07:00,950 relative to electrodes and neurons that you might be very interested in. 120 00:07:00,950 --> 00:07:06,050 The Utah electrode array is a very small array made from silicone that has ten 121 00:07:06,050 --> 00:07:07,950 electrodes by ten electrodes. 122 00:07:07,950 --> 00:07:09,560 Each electrode is like a tiny needle. 123 00:07:09,560 --> 00:07:14,550 It's made from silicon, it is conductive, it's connected to an individual line. 124 00:07:14,550 --> 00:07:19,050 If you look at this big kind of gold line right here, that has 100 little different 125 00:07:19,050 --> 00:07:23,650 lines, about [INAUDIBLE] of hair that come back to a central system. 126 00:07:23,650 --> 00:07:28,370 This electrode array can be placed in or in contact with any nerve. 127 00:07:28,370 --> 00:07:32,000 For example, it could be stuck on the surface of the brain. 128 00:07:32,000 --> 00:07:34,430 This can be used to either receive from the nerves and 129 00:07:34,430 --> 00:07:38,310 be able to read their signals, or it can be used to stimulate them. 130 00:07:38,310 --> 00:07:42,420 This Utah electrode array is being put into commercial products to help blind 131 00:07:42,420 --> 00:07:47,450 people see, deaf people hear, and people who have lost the use of their limbs 132 00:07:47,450 --> 00:07:53,120 to be able to regain that use or to be able to use bionic limbs as a substitute. 133 00:07:53,120 --> 00:07:55,250 Very, very interesting research going on right now. 134 00:07:56,960 --> 00:07:58,690 Now let's talk about power. 135 00:07:58,690 --> 00:08:02,100 Power is given in watts, that is voltage times current. 136 00:08:02,100 --> 00:08:07,120 So watts is volts times amps, so p is equal to VI. 137 00:08:07,120 --> 00:08:10,189 Power is also the time rate of change of energy. 138 00:08:10,189 --> 00:08:11,894 DW is not watts. 139 00:08:11,894 --> 00:08:14,907 DW is energy, as the change of energy per time, and 140 00:08:14,907 --> 00:08:17,580 that would be the power as a function of time. 141 00:08:19,380 --> 00:08:23,160 The passive sign convention tells us if a device is consuming power or 142 00:08:23,160 --> 00:08:24,500 producing power. 143 00:08:24,500 --> 00:08:27,028 Here's how the passive sign convention works. 144 00:08:27,028 --> 00:08:32,009 Define a device, shown here as the dark blue box, and one side of the device is a, 145 00:08:32,009 --> 00:08:33,270 the other side is b. 146 00:08:33,270 --> 00:08:39,150 Vab is the potential across that device, might be positive, might be negative. 147 00:08:39,150 --> 00:08:42,780 Then define the current going into the device in the direction shown here, 148 00:08:42,780 --> 00:08:44,390 from plus to minus. 149 00:08:44,390 --> 00:08:46,785 The current is always defined as positive in this way. 150 00:08:48,850 --> 00:08:50,460 Here's an example. 151 00:08:50,460 --> 00:08:52,010 Here's the battery with a resistor. 152 00:08:52,010 --> 00:08:55,510 I've chosen a single resistor here just for your simplicity. 153 00:08:55,510 --> 00:09:00,100 The current, and we calculated this in Multisim before, is the voltage divided by 154 00:09:00,100 --> 00:09:05,920 the resistance, or 1.5 milliamps in this case if we have a 1.5 volt battery. 155 00:09:05,920 --> 00:09:07,500 Now, let's look over here and 156 00:09:07,500 --> 00:09:10,720 determine what the voltage across that resistor is going to be. 157 00:09:10,720 --> 00:09:12,790 The voltage is going to be IR. 158 00:09:12,790 --> 00:09:16,055 I is 1.5 milliamps, the resistance is 1 kiloohms, 159 00:09:16,055 --> 00:09:19,184 so the voltage across that resistor is 1.5 volts. 160 00:09:20,310 --> 00:09:22,550 Now, let's see what happens with the power. 161 00:09:22,550 --> 00:09:26,060 Let's first calculate the power here on the right, for the resistor. 162 00:09:26,060 --> 00:09:29,780 Well, here's our device, this resistor, and 163 00:09:29,780 --> 00:09:33,920 the voltage across it is 1.5 volts, positive 1.5 volts. 164 00:09:33,920 --> 00:09:37,700 And the current is positive 1.5 milliamps. 165 00:09:37,700 --> 00:09:44,430 So the power is going to be 1.5 volts times 1.5 milliamps or 2.25 milliwatts. 166 00:09:44,430 --> 00:09:48,100 Since the power is positive, the resistor is consuming power. 167 00:09:48,100 --> 00:09:49,020 That is what we expect. 168 00:09:49,020 --> 00:09:54,510 In fact, resistors consume power and convert it into heat or light energy. 169 00:09:54,510 --> 00:09:56,290 Now, let's come over to this side. 170 00:09:56,290 --> 00:09:59,523 We know intrinsically that the battery must be producing power. 171 00:09:59,523 --> 00:10:02,006 Let's see if that happens mathematically. 172 00:10:02,006 --> 00:10:06,086 When we're looking at this, we're going to consider this to be our device, and 173 00:10:06,086 --> 00:10:10,450 the current is coming into the device in the positive to negative direction. 174 00:10:10,450 --> 00:10:14,020 The current, in this way, is 1.5 milliamps positive. 175 00:10:14,020 --> 00:10:18,510 The voltage, if we're looking at it in this direction, from bottom to top, not 176 00:10:18,510 --> 00:10:24,200 from top to bottom, from bottom to top, the voltage is going to be -1.5 volts. 177 00:10:24,200 --> 00:10:29,390 So the power is equal to -1.5 volts times +1.5 milliamps for 178 00:10:29,390 --> 00:10:32,580 a total of -2.25 milliwatts. 179 00:10:32,580 --> 00:10:34,440 Remember, if the power is negative, 180 00:10:34,440 --> 00:10:38,780 that means that the device is producing power instead of using power. 181 00:10:38,780 --> 00:10:43,520 Another important feature of powers, the power has to be conserved within a system. 182 00:10:43,520 --> 00:10:46,460 There's no place for loose power to be hanging out. 183 00:10:46,460 --> 00:10:51,298 So we can see that our power that's produced is -2.25 milliwatts, the power 184 00:10:51,298 --> 00:10:56,571 that is used is 2.25 milliwatts, and these two things have to be equal and opposite. 185 00:10:58,536 --> 00:11:00,630 Now, let's talk about the energy. 186 00:11:00,630 --> 00:11:04,070 The energy and the picture that we use for 187 00:11:04,070 --> 00:11:09,330 that is W, the variable we use is W, that's given in Joules or kilowatt hours. 188 00:11:09,330 --> 00:11:12,818 Most of the things that we use to measure in electrical engineering are kilowatt 189 00:11:12,818 --> 00:11:13,338 hours, but 190 00:11:13,338 --> 00:11:16,788 most of the things mechanical engineers will be talking about will be joules. 191 00:11:16,788 --> 00:11:24,001 They are the same thing. 192 00:11:24,001 --> 00:11:27,777 The energy is the integration over time of the power. 193 00:11:27,777 --> 00:11:32,277 That means that we take the power, and all the power that we might have used all day, 194 00:11:32,277 --> 00:11:35,450 if t is our day, is going to tell us how much energy we used. 195 00:11:35,450 --> 00:11:38,900 1 joule is equal to 1 watt second, so 196 00:11:38,900 --> 00:11:42,145 let's see what 1 kilowatt hour is equal to. 197 00:11:42,145 --> 00:11:47,010 1 kilowatt hour, and let's balance our units, I need a watt on the bottom and 198 00:11:47,010 --> 00:11:49,785 an hour on the bottom in order to cancel these out. 199 00:11:49,785 --> 00:11:52,704 1 kilowatt hour times 1 joule per watt seconds, 200 00:11:52,704 --> 00:11:56,320 times 60 seconds per minute, 60 minutes per hour. 201 00:11:56,320 --> 00:11:59,199 My minutes cancel out, my seconds cancel out. 202 00:11:59,199 --> 00:12:04,109 My watt hours cancel out, leaving me with Joules and this k over here, so 203 00:12:04,109 --> 00:12:06,052 I get 3600 kilojoules. 204 00:12:06,052 --> 00:12:09,703 1 kWh is 3600 kilojoules. 205 00:12:11,230 --> 00:12:16,180 Now, let's figure out what energy you need, how much energy do you need? 206 00:12:16,180 --> 00:12:20,110 This is a picture of the Internet base station on the mountain above my house. 207 00:12:20,110 --> 00:12:21,840 It's a solar-powered base station. 208 00:12:21,840 --> 00:12:25,140 The power is stored in car batteries, 12 volt batteries. 209 00:12:25,140 --> 00:12:28,080 And then the base station, that's the little antenna right there, 210 00:12:28,080 --> 00:12:30,750 is a line of site base station over the Park City for 211 00:12:30,750 --> 00:12:34,120 mountain peak to mountain peak several miles away. 212 00:12:34,120 --> 00:12:37,180 In order to figure out how much solar panel you need, 213 00:12:37,180 --> 00:12:40,440 you first are going to make your device as efficient as possible. 214 00:12:40,440 --> 00:12:42,365 Figure out how many kilowatts you need. 215 00:12:42,365 --> 00:12:45,971 Then you're gong to decide how many hours that needs to be able to run. 216 00:12:45,971 --> 00:12:48,435 Now, when you're considering the number of hours, 217 00:12:48,435 --> 00:12:51,995 you want to consider how much time you can actually charge your solar panels, 218 00:12:51,995 --> 00:12:56,160 which obviously is only during the day, and a fact that it's only the good days. 219 00:12:56,160 --> 00:12:59,890 So if you have dark rainy days, you need to have enough power stored up. 220 00:12:59,890 --> 00:13:04,320 So you take the number of hours, you multiply the number of appliances in 221 00:13:04,320 --> 00:13:08,980 kilowatts times the number of hours you plan to use those devices, and 222 00:13:08,980 --> 00:13:11,250 add it up to get kilowatt hours. 223 00:13:11,250 --> 00:13:16,480 Consider the recharge time for night, dark or snowy days, etc. 224 00:13:16,480 --> 00:13:19,470 I put some interesting links online so that you could calculate this for 225 00:13:19,470 --> 00:13:21,690 an application of your interest, or 226 00:13:21,690 --> 00:13:24,950 perhaps figure out just how much power you're using in your own home. 227 00:13:26,830 --> 00:13:30,630 So our summary of voltage and power is we talked about what is voltage and 228 00:13:30,630 --> 00:13:31,940 how you measure it. 229 00:13:31,940 --> 00:13:36,450 It's polarity, the impact of using a ground and where you place the ground, and 230 00:13:36,450 --> 00:13:38,620 what is power, and what is energy. 231 00:13:38,620 --> 00:13:41,109 Then we talked about some interesting real applications. 232 00:13:42,270 --> 00:13:45,115 Now, here is, you've wondered what is on the front side. 233 00:13:45,115 --> 00:13:47,930 Here's the Solar Powered Neighborhood Internet Base Station 234 00:13:47,930 --> 00:13:49,390 at the top of Emigration Canyon. 235 00:13:50,520 --> 00:13:54,486 The view from above, over to Park City, you can see the mountain top that 236 00:13:54,486 --> 00:13:58,209 it's transmitting to and receiving from is quite a distance away. 237 00:13:58,209 --> 00:14:00,239 How do you get all that stuff up there, and 238 00:14:00,239 --> 00:14:03,496 why do you care about the number of solar panels and the batteries? 239 00:14:03,496 --> 00:14:08,730 Well, it's 200 pounds of car batteries carried up by people and by horses. 240 00:14:08,730 --> 00:14:11,010 As well as the base station that you can see right here, 241 00:14:11,010 --> 00:14:14,070 a couple of the neighbors carrying that up on a pole. 242 00:14:14,070 --> 00:14:16,061 If you have to carry all of this stuff to the top of the mountain, 243 00:14:16,061 --> 00:14:20,190 you are going to carry as few solar panels and as few batteries as possible. 244 00:14:21,270 --> 00:14:24,930 So now, take a look at your own applications, find something interesting, 245 00:14:24,930 --> 00:14:29,090 and estimate the amount of solar power that you would need for that application.