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