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Voltage, Electric Energy, and Capacitors - Crash Course Physics #27
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00:00:03.060 --> 00:00:05.480 You may have seen this many times on TV. 00:00:05.480 --> 00:00:12.380 A person collapses in a hospital, and the doctor rushes with his hands in shock, putting them on his chest and shouting: "Caution!" 00:00:12.380 --> 00:00:14.540 After the trauma, the patient was rescued. 00:00:14.540 --> 00:00:16.239 That life-saving technology is real. 00:00:16.239 --> 00:00:21.200 It operates on two major electrical laws: capacitance and electric potential energy. 00:00:21.200 --> 00:00:26.240 These two bumps are part of the defibrillator, which is basically just a great intense. 00:00:26.250 --> 00:00:31.370 It uses the electrical charge to store energy, and then empties it into the patient’s body. 00:00:31.370 --> 00:00:36.860 The current stops the turbulent contractions of the cardiac muscle, and gives the heart an opportunity to beat properly. 00:00:36.860 --> 00:00:40.540 Prepare, because this lesson has the power to save lives. 00:00:40.540 --> 00:00:52.420 [Badge] 00:00:52.420 --> 00:00:57.640 To find out how a capacitor can save a life, let's review what capacitors are and how they work. 00:00:57.640 --> 00:01:02.880 The capacitor consists of two parallel conductive plates, opposite to the charge, and between them an electric field. 00:01:02.880 --> 00:01:07.200 This arrangement allows the capacitor to store energy, in the form of potential electrical energy. 00:01:07.200 --> 00:01:11.380 The element also has gravitational potential energy when lifted from the ground, 00:01:11.380 --> 00:01:16.060 The charged element also has electric potential energy, when placed in an electric field. 00:01:16.060 --> 00:01:21.580 In either case, the potential energy can be used to do work, when the force is applied at a distance. 00:01:21.580 --> 00:01:26.759 But how can you determine the amount of energy in a system, and how much work can it do? 00:01:26.760 --> 00:01:33.840 As in the defibrillator, you want enough energy to stop the pulse disorder, but without causing harm. 00:01:33.840 --> 00:01:40.160 To measure the potential energy of an electric field, imagine a positive test charge moving between the capacitor plates. 00:01:40.160 --> 00:01:47.619 When placed between the two panels, the uniform electric field generates constant force towards the negative plate. 00:01:47.620 --> 00:01:57.320 If the charge is released from the positive plate towards the electric force, the work is calculated by multiplying the force by the distance between the two plates. 00:01:57.320 --> 00:02:01.940 We also know that this force is equal to the value of the test charge multiplied by the electric field. 00:02:01.940 --> 00:02:10.320 We can apply equal and opposite force to the charged object and move it through the capacitor slowly so that we neglect the kinetic energy of the particle. 00:02:10.320 --> 00:02:15.239 And because of what we know about the energy-labor theory and the energy conservation law, 00:02:15.240 --> 00:02:22.300 We know that the change in potential energy is equal to the action of the external force, or the negative action of the electric force. 00:02:22.300 --> 00:02:27.580 So we found a decrease in the potential energy of a single point charge in a uniform electrical field. 00:02:27.580 --> 00:02:36.800 The decrease in potential energy over the amount of the test charge gives us the difference of potential electrical energy in one charge, also known as the electric potential. 00:02:36.800 --> 00:02:43.240 The electric potential depends on the electric field and position, and does not depend on the value of the test charge. 00:02:43.250 --> 00:02:48.209 The units of electric potential are joules on coulombs, known as volts. 00:02:48.209 --> 00:02:54.420 The electric potential difference is also called tension, and is just another way to describe the potential decrease. 00:02:54.420 --> 00:03:01.179 When expressed mathematically, the tension is equal to the electric field multiplied by the two capacitor plates. 00:03:01.180 --> 00:03:07.440 We used the default test charge to describe the amount of tension in the charged capacitor. 00:03:07.440 --> 00:03:12.640 Let us put our new terminology to the test now, to find the difference of electric potential in a realistic scenario. 00:03:12.640 --> 00:03:21.238 Let's say that the capacitor has a 1 mm capacitance and its electrical field is 1000 Newtons per coulomb, which means 1,000 volts per meter. 00:03:21.240 --> 00:03:29.980 The electric field can be found by dividing the force by charge, or Newton by the coulomb, as well as the tension over the distance, or volts per meter. 00:03:29.980 --> 00:03:31.540 All represent the same value. 00:03:31.540 --> 00:03:35.480 Let's say we divided 1000 volts per meter by 1 mm. 00:03:35.480 --> 00:03:38.399 We find that the tension of the capacitor is 1 volt. 00:03:38.400 --> 00:03:46.680 Since the capacitor generates a uniform field, we assume that the wattage is constant and is in the direction of the movement of the test charge. 00:03:46.680 --> 00:03:49.680 As it moves, the latency decreases more and more. 00:03:49.680 --> 00:03:56.180 The hypotension can be represented by drawing lines at locations where the tension of the test charges is equal. 00:03:56.180 --> 00:03:58.440 These are known as equal-latency lines. 00:03:58.440 --> 00:04:06.560 In the capacitor, the lines parallel the plates, and the latency of the line closest to the negative plate decreases and its tension decreases. 00:04:06.560 --> 00:04:10.420 These equal-latency lines always parallel the electric field. 00:04:10.420 --> 00:04:16.500 We learned to calculate the electric potential of capacitors, but can we apply that to point charges? 00:04:16.510 --> 00:04:19.670 We know the equation for the electric field generated by a point charge. 00:04:19.670 --> 00:04:25.540 Since there is no electric field regularly with a capacitor field, we cannot use the same equations. 00:04:25.540 --> 00:04:35.139 Finding the field resulting from the raster charge is similar to finding the difference of energy inherent in one charge, between the spot adjacent to the raster charge and an unknown location at infinity. 00:04:35.140 --> 00:04:45.000 If a small element is charged near our Q point, it will start with a high potential and decrease as it moves away. 00:04:45.060 --> 00:04:51.400 So we can calculate the total potential energy, by integrating the negative field from zero to infinity. 00:04:51.400 --> 00:04:56.460 We have an equation that describes the electric potential produced by any point charge. 00:04:56.460 --> 00:05:01.039 We can precisely plot the equal-latency lines of the point charges as we did in the capacitor. 00:05:01.040 --> 00:05:06.660 In a point charge, the equal-latency lines appear as circles that increase around the charged particle. 00:05:06.660 --> 00:05:09.280 The higher the distance from the point charge, the lower the tension. 00:05:09.280 --> 00:05:16.880 For a bipolar electrical molecule, which consists of two positive and negative point charges, the potentials from each charge can be collected. 00:05:16.880 --> 00:05:21.040 Here you will see, that each isometric line is not at a fixed distance from a point charge. 00:05:21.040 --> 00:05:24.420 This is because you have two point charges, each with a special electric field. 00:05:24.420 --> 00:05:31.380 So a test charge to the right of the positive point charge will not have the same latency as another at the same distance at the opposite end. 00:05:31.389 --> 00:05:33.920 Let us now return to the potential energy and capacitors. 00:05:33.920 --> 00:05:39.820 As it is the biggest reason why capacitors are useful from defibrillator to electronic vehicles: 00:05:39.820 --> 00:05:43.760 When a capacitor plate stores an electrical charge, it actually stores energy! 00:05:43.760 --> 00:05:51.080 If a battery reaches a primary circuit containing a capacitor, it moves the charge from one plate to another through a conductive wire. 00:05:51.080 --> 00:05:54.399 This leads to a positive charge plate, and a negative charge plate. 00:05:54.400 --> 00:06:01.318 But the capacitor did not gain a total charge, the positive and negative charges on both boards are equal. 00:06:01.320 --> 00:06:10.760 The battery uses its potential as a generator to convert its tension into tension in the capacitor, which gives it latent energy. 00:06:10.760 --> 00:06:16.360 In a defibrillator, this energy quickly converts from potential energy into electrical shock that crosses the body. 00:06:16.360 --> 00:06:20.779 If you are trying to save a soul, you must get the right amount of energy from the condenser. 00:06:20.780 --> 00:06:29.880 To measure the charge stored in the capacitor, a battery in the circuit can be used to create tension between the plates, then divide the charge in each plate by that tension. 00:06:29.880 --> 00:06:34.540 This value is known as the capacitance, the amount of charge that a capacitor can hold. 00:06:34.540 --> 00:06:39.380 Capacitance is measured in farads, where farads equals Coulomb over a Volt. 00:06:39.380 --> 00:06:46.460 The capacitance values are usually low, so we talk about capacitors using microfarad and nanofarad. 00:06:46.469 --> 00:06:50.169 The capacitance is determined by the size and shape of the capacitor. 00:06:50.169 --> 00:07:00.829 One way of expressing capacitance is by dividing the area of each plate by the distance between them, and multiplying that by a constant, known as the permittivity of free space, is indicated by the psalone note. 00:07:00.829 --> 00:07:06.520 By enlarging or rounding the panels, the space for more charge expands, producing a heavier electrical field. 00:07:06.520 --> 00:07:10.620 Once you determine the geometry of the two panels, the capacitance does not change. 00:07:10.629 --> 00:07:14.369 Unless you put something in between, the amplitude increases. 00:07:14.369 --> 00:07:19.349 This thing is called a buffer. Typically, it is an insulating material, such as plastic and glass. 00:07:19.349 --> 00:07:24.169 The insulator is used to increase capacitance, at the same time, to prevent any charge from jumping from one plate to another. 00:07:24.169 --> 00:07:32.000 Sometimes, when the plates heat up or the tension rises, the electrons naturally jump between the plates, reducing the amount of charge stored. 00:07:32.000 --> 00:07:34.979 So the dielectric prevents electrons from crossing the gap. 00:07:34.980 --> 00:07:41.880 It is usually best to bring the panels closer together without contact, since the decreasing distance increases the capacitance. 00:07:41.880 --> 00:07:46.900 So, with a very thin dielectric, the distance decreases while the two plates remain separate. 00:07:46.900 --> 00:07:53.700 The molecules that make up the dielectric are polar, which means that one side of the molecule is positive while the other is negative. 00:07:53.700 --> 00:08:03.820 The particles line up along the electric field and generate their own field in the opposite direction, leading to a weaker total field, while the two plates retain the same amount of charge. 00:08:03.820 --> 00:08:13.200 By inserting an insulating material into the capacitor, we increased the capacitance, and we were able to store more charge and energy with the same tension. 00:08:13.200 --> 00:08:17.119 For this the full capacitance equation contains a dielectric constant, K. 00:08:17.119 --> 00:08:20.419 So the dielectric condensers help store more energy. 00:08:20.420 --> 00:08:25.780 And that potential energy is actually stored inside the electric field between the two capacitor plates. 00:08:25.780 --> 00:08:34.380 We can calculate the potential energy stored in this field, by integrating the tension on the charge of the two plates, which decreases up to half the charge multiplied by tension. 00:08:34.380 --> 00:08:40.259 However, when using a capacitor, it is useful to calculate the energy stored in an electric field in one volumetric unit. 00:08:40.260 --> 00:08:50.120 We often want to know the amount of energy present in a specific place, between the panels, for example, so we use the energy density, or the amount of energy stored in the field by one volume. 00:08:50.120 --> 00:08:58.900 We can calculate the energy density associated with an electric field at any point or vacuum, by dividing the potential energy by the volume between the two plates. 00:08:58.900 --> 00:09:04.620 Using algebra, we find that this ends in half the Absolon Note multiplied by the square of the electric field. 00:09:04.620 --> 00:09:07.820 This relationship remains valid in any vacuum that has an electric field. 00:09:07.820 --> 00:09:16.600 Now that we know all this, the doctor can verify that the defibrillator is ready to use. 00:09:17.720 --> 00:09:20.040 Today we learned a lot! 00:09:20.040 --> 00:09:24.339 We talked about the potential energy, and how it differs from electrical potential, or tension. 00:09:24.340 --> 00:09:28.560 We discussed how capacitors work, and the factors that determine how much charge you have. 00:09:28.560 --> 00:09:34.020 We also learned how to increase storage space, and calculate the potential energy of any capacitor. 00:09:34.020 --> 00:09:38.000 The Crash Course Physics series was produced in association with PBS Digital Studios. 00:09:38.000 --> 00:09:42.320 You can head over to their channel and check out the latest episodes from shows like: 00:09:42.320 --> 00:09:45.720 First Person, PBS Off Book Game Show, this episode was filmed 00:09:45.720 --> 00:09:49.760 In Doctor Cheryl C. 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