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Capacitor Tutorial, Basic Introduction, Capacitance Explained - How it works, Dielectrics, Physics
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00:00:00.030 in this video we're going to talk about 00:00:02.00000:00:02.010 capacitors so what exactly is a 00:00:04.49000:00:04.500 capacitor a capacitor stores electrical 00:00:08.57000:00:08.580 charge it's not the same as a battery a 00:00:13.90000:00:13.910 capacitor uses two metal plates 00:00:16.77900:00:16.789 separated by an insulator and it 00:00:21.23000:00:21.240 basically stores charge by taking 00:00:23.75000:00:23.760 electrons from one side and pumping it 00:00:25.70000:00:25.710 towards the other side the insulator 00:00:29.92900:00:29.939 could be air it could be paper it could 00:00:32.60000:00:32.610 be water anything that doesn't conduct 00:00:35.66000:00:35.670 electricity could be the insulator so 00:00:37.79000:00:37.800 that's basically what a capacitor is 00:00:39.04900:00:39.059 it's made of two metal plates separated 00:00:41.69000:00:41.700 by an insulator and it stores electrical 00:00:44.18000:00:44.190 charge now there are some equations they 00:00:46.54900:00:46.559 need to be familiar with Q is equal to 00:00:50.09000:00:50.100 cv q stands for the charge and the 00:00:56.72000:00:56.730 electric charge is measured in the units 00:00:58.52000:00:58.530 kaloumes one klum is equal to one amp 00:01:06.20000:01:06.210 times one second so Q is equal to I T 00:01:13.84000:01:13.850 where I is the electric current in amps 00:01:18.14000:01:18.150 t is the time in seconds now C 00:01:22.45000:01:22.460 represents the capacitance and the 00:01:28.67000:01:28.680 capacitance is measured in farad's V is 00:01:33.80000:01:33.810 the voltage measured in volts so what 00:01:38.66000:01:38.670 exactly is capacitance how can we 00:01:41.06000:01:41.070 describe it I like to think of 00:01:44.14900:01:44.159 capacitance in terms of charge 00:01:46.19000:01:46.200 efficiency one farad is equal to one 00:01:51.35000:01:51.360 Coulomb per volt so let's say if we have 00:01:58.24900:01:58.259 two capacitors one has a capacitance of 00:02:02.12000:02:02.130 10 farad's and the other one has 00:02:04.31000:02:04.320 capacitance of 2 farad's 00:02:06.24900:02:06.259 let's call the first one capacitor a and 00:02:08.99000:02:09.000 the second one capacitor B 00:02:12.70000:02:12.710 now if we charge up capacitor a to a 00:02:17.18000:02:17.190 voltage of let's say 1 volt it can store 00:02:20.63000:02:20.640 10 kaloumes of charge for capacitor beam 00:02:26.39000:02:26.400 if we charge it up to 1 volt it can only 00:02:28.91000:02:28.920 store 2 coulombs of charge now what if 00:02:32.24000:02:32.250 we increase the voltage let's say if we 00:02:34.58000:02:34.590 charge up to 2 volts 00:02:36.13000:02:36.140 capacitor a can hold 20 Klum's of charge 00:02:40.84000:02:40.850 capacitor beam if we charge it up to 2 00:02:43.55000:02:43.560 volts if we connect it to a 2 volt 00:02:45.14000:02:45.150 battery it can hold up to 4 coulombs of 00:02:47.99000:02:48.000 charge so as you can see capacitance is 00:02:52.57000:02:52.580 basically charged efficiency it's how 00:02:55.64000:02:55.650 much charge you can hold per volt as you 00:03:00.05000:03:00.060 increase the voltage you can hold more 00:03:01.70000:03:01.710 charge but if you look at capacitor a 00:03:04.88000:03:04.890 it's more efficient it can hold 10 00:03:07.04000:03:07.050 kaloumes of charge for 1 volt whereas 00:03:09.95000:03:09.960 capacitor B can only hold 2 coulombs of 00:03:13.04000:03:13.050 charge per volt so the higher 00:03:15.83000:03:15.840 capacitance means that that you can 00:03:18.32000:03:18.330 restore more charge per volt now Q is 00:03:24.53000:03:24.540 equal to C V if you increase the voltage 00:03:27.14000:03:27.150 the charge will increase as you can see 00:03:29.84000:03:29.850 here however if you increase the voltage 00:03:34.72900:03:34.739 the capacitance doesn't increase the 00:03:37.72000:03:37.730 capacitance is based on the construction 00:03:40.72900:03:40.739 of the capacitor it doesn't depend on 00:03:42.92000:03:42.930 the voltage so make sure you understand 00:03:46.22000:03:46.230 that the capacitance is constant and it 00:03:49.49000:03:49.500 only depends on the construction of the 00:03:51.53000:03:51.540 capacitor now going back to the equation 00:03:54.19900:03:54.209 Q equals C V let's talk about electric 00:03:57.56000:03:57.570 charge we need to understand that 00:03:59.78000:03:59.790 electric charge is associated with the 00:04:02.63000:04:02.640 plaza T of charge particles and in the 00:04:06.22900:04:06.239 case of metals electrons are basically 00:04:08.54000:04:08.550 the charge carriers they're the ones 00:04:10.34000:04:10.350 that are free to move inside a metal the 00:04:12.92000:04:12.930 protons are fixed in place so the 00:04:16.07000:04:16.080 electric charge is equal to the number 00:04:19.40000:04:19.410 of electrons times the charge of each 00:04:21.74000:04:21.750 electron 00:04:22.76000:04:22.770 now the charge of each electron is 00:04:25.07000:04:25.080 negative one point six times 10 to the 00:04:28.12900:04:28.139 negative 19 coulombs so this charge is 00:04:32.54000:04:32.550 discrete that's the lowest charge that 00:04:34.87900:04:34.889 an electron can have every electron has 00:04:37.10000:04:37.110 that charge you can have a charge that's 00:04:39.14000:04:39.150 less than this number unless you have a 00:04:41.83900:04:41.849 fraction of an electron so charge is 00:04:45.89000:04:45.900 quantized now you need to know that the 00:04:53.83900:04:53.849 unit volt is one Joule per Coulomb 00:05:00.30900:05:00.319 electric potential represented by Z is 00:05:04.18000:05:04.190 basically the ratio between the electric 00:05:06.40900:05:06.419 potential energy and the charge Q now be 00:05:11.54000:05:11.550 careful electric potential and voltage 00:05:15.08000:05:15.090 are not necessarily the same thing 00:05:17.93000:05:17.940 but they're similar the voltage is the 00:05:22.79000:05:22.800 difference in the electric potentials of 00:05:25.30900:05:25.319 two points so voltage is Delta V is the 00:05:32.62900:05:32.639 change in electric potential VB is the 00:05:37.15900:05:37.169 electric potential at position B VA is 00:05:39.92000:05:39.930 the electric potential a position eight 00:05:42.39900:05:42.409 so electric potential is the electric 00:05:45.58900:05:45.599 potential energy per charge now electric 00:05:48.89000:05:48.900 potential and voltage - both measured in 00:05:50.74900:05:50.759 volts 00:05:51.11000:05:51.120 so it's joules per Coulomb which is one 00:05:53.42000:05:53.430 volt the voltage is basically the ratio 00:06:00.77000:06:00.780 between the work and the charge it's the 00:06:04.73000:06:04.740 amount of work that can be done per unit 00:06:06.26000:06:06.270 charge so work is equal to Q Delta V and 00:06:11.42000:06:11.430 I believe there's a negative sign 00:06:12.29000:06:12.300 somewhere 00:06:15.37000:06:15.380 now let's get back to capacitance we 00:06:18.49900:06:18.509 said that the unit of capacitance is the 00:06:20.57000:06:20.580 farad one farad is a very very large 00:06:23.87000:06:23.880 number and only super capacitors have 00:06:27.40900:06:27.419 this much capacitance most common 00:06:31.04000:06:31.050 capacitors that you may see like the 00:06:32.45000:06:32.460 electrolytic capacitors they might be in 00:06:34.87900:06:34.889 the area of a 00:06:36.26000:06:36.270 micro farad can be 10 100 microfarad you 00:06:40.19000:06:40.200 have some capacitors that are like nano 00:06:41.90000:06:41.910 farad and even some in the Pico farad 00:06:44.54000:06:44.550 level a micro farad is 1 times 10 to the 00:06:47.84000:06:47.850 minus 6 rats 00:06:49.15000:06:49.160 nano is 10 to minus 9 Pico is 10 to 00:06:54.62000:06:54.630 minus 12 00:07:01.12000:07:01.130 now there's another equation that you 00:07:03.05000:07:03.060 need to know C is equal to epsilon sub 00:07:07.22000:07:07.230 naught times a divided by D we said that 00:07:10.73000:07:10.740 the capacitance is basically a measure 00:07:14.87000:07:14.880 it's basically it's dependent on the 00:07:17.36000:07:17.370 construction of the capacitor so let's 00:07:22.07000:07:22.080 draw a capacitor here we have two metal 00:07:24.56000:07:24.570 plates separated by a distance D each 00:07:34.07000:07:34.080 plate has an area a and for a rectangle 00:07:37.76000:07:37.770 area is just a lifetime's with the 00:07:41.12000:07:41.130 capacitance depends on the area if you 00:07:45.17000:07:45.180 increase the area the capacitance of the 00:07:47.66000:07:47.670 capacitor will increase because you can 00:07:50.00000:07:50.010 store more charge over a larger surface 00:07:54.79000:07:54.800 now if you increase the distance the 00:07:58.22000:07:58.230 capacitance will decrease given the same 00:08:02.51000:08:02.520 amount of charge if you increase the 00:08:04.01000:08:04.020 distance then the strength of the 00:08:07.04000:08:07.050 electric field between the two plates 00:08:08.66000:08:08.670 will decrease and therefore the electric 00:08:12.08000:08:12.090 force acted on the charges in between 00:08:14.33000:08:14.340 the plates if there is a charge will be 00:08:16.52000:08:16.530 weaker and also the capacitance will go 00:08:20.30000:08:20.310 down as well so make sure you understand 00:08:23.69000:08:23.700 this if you increase the area with the 00:08:25.73000:08:25.740 pass fence will increase you increase 00:08:27.29000:08:27.300 the distance the capacitance will 00:08:29.36000:08:29.370 decrease now sometimes you can add an 00:08:34.40000:08:34.410 insulator the insulator doesn't have to 00:08:38.39000:08:38.400 be air and if you add an insulator also 00:08:42.14000:08:42.150 known as a dielectric the equation will 00:08:44.27000:08:44.280 change C will be equal to K times 00:08:49.55000:08:49.560 Epsilon 00:08:50.36000:08:50.370 times a over D now let's not forget this 00:08:54.41000:08:54.420 little zero here so K is the dielectric 00:08:57.56000:08:57.570 constant and for air K is about one 00:09:02.39000:09:02.400 point zero zero zero six is very small 00:09:04.91000:09:04.920 very close to one for a pure vacuum 00:09:07.57900:09:07.589 where there's nothing no gas molecules K 00:09:10.51900:09:10.529 is exactly one for other substances K 00:09:14.60000:09:14.610 will increase for example and say if we 00:09:16.46000:09:16.470 have quartz so this material K is about 00:09:25.75000:09:25.760 four point three in the case of water K 00:09:31.91000:09:31.920 is about eighty now what effect does the 00:09:37.55000:09:37.560 dielectric have on a capacitance as you 00:09:43.88000:09:43.890 increase K the capacitance will increase 00:09:46.42000:09:46.430 so it's very useful to use a dielectric 00:09:49.15000:09:49.160 you can store more charge per volt C is 00:09:56.03000:09:56.040 equal to K times C sub naught where C 00:10:00.14000:10:00.150 sub naught is the original capacitance 00:10:01.67000:10:01.680 without a dielectric and C is the 00:10:05.48000:10:05.490 capacitance with the dielectric so 00:10:10.04000:10:10.050 anytime you add a dielectric the 00:10:12.23000:10:12.240 capacitance will go up however the 00:10:13.79000:10:13.800 voltage will go down V is equal to the 00:10:17.78000:10:17.790 original voltage divided by K so let's 00:10:21.38000:10:21.390 say if you have a capacitor that has ten 00:10:26.81000:10:26.820 frats and let's say the voltage across 00:10:29.72000:10:29.730 it is 20 volts and the dielectric is one 00:10:34.40000:10:34.410 let's say if air in between it now let's 00:10:38.60000:10:38.610 say if we add a material and the 00:10:40.61000:10:40.620 dielectric has a constant of - I mean 00:10:44.93000:10:44.940 the insulator has a dielectric constant 00:10:46.88000:10:46.890 - the capacitance will increase the 20 00:10:51.01000:10:51.020 of the voltage will decrease the 10 so 00:10:56.72000:10:56.730 by increasing the dielectric you will 00:10:58.79000:10:58.800 increase the capacitance but you will 00:11:00.98000:11:00.990 decrease the voltage proportionately 00:11:02.98000:11:02.990 but notice that the total charge remains 00:11:05.62000:11:05.630 the same now you have to do this when 00:11:09.10000:11:09.110 the capacitor is charged but not 00:11:11.41000:11:11.420 connected to a battery because if you 00:11:14.44000:11:14.450 decrease the voltage of a capacitor and 00:11:16.09000:11:16.100 if it's connected to a battery then 00:11:18.79000:11:18.800 charge will flow from the battery to the 00:11:21.16000:11:21.170 capacitor bringing its voltage back up 00:11:24.19000:11:24.200 to 20 so you have to charge the 00:11:27.69900:11:27.709 capacitor first let's say if it's 00:11:29.71000:11:29.720 charged to a voltage of 20 then 00:11:31.84000:11:31.850 disconnect the battery and the capacitor 00:11:33.67000:11:33.680 and then add the dielectric when you add 00:11:36.97000:11:36.980 the dielectric when the capacitor is not 00:11:39.51900:11:39.529 connected to the battery the charge of 00:11:41.86000:11:41.870 the capacitor will remain the same the 00:11:44.76900:11:44.779 capacitance will increase with the new 00:11:46.48000:11:46.490 dielectric but the voltage will decrease 00:11:49.56000:11:49.570 so kiwigal ceasing notice that if we 00:11:52.75000:11:52.760 multiply 10 by 20 we're going to get a 00:11:55.36000:11:55.370 charge of 200 and that is 200 kaloumes 00:12:01.13900:12:01.149 if we multiply 20 by 10 we will still 00:12:06.40000:12:06.410 get the same charge of 200 kaloumes so 00:12:11.62000:12:11.630 by adding a dielectric to a charged 00:12:14.53000:12:14.540 capacitor 1 is not connected to a 00:12:16.09000:12:16.100 battery the capacitance will increase 00:12:18.19000:12:18.200 and the voltage will decrease now I do 00:12:21.69900:12:21.709 want to mention something the equation 00:12:23.82900:12:23.839 that we had that I drew on the board 00:12:27.01000:12:27.020 that look like this this is the 00:12:29.65000:12:29.660 capacitance of a capacitor if a vacuum 00:12:33.88000:12:33.890 is used as a dielectric if there's 00:12:35.41000:12:35.420 nothing in between the two metal plates 00:12:37.88900:12:37.899 now the equation changes to this if you 00:12:44.44000:12:44.450 have a dielectric it's going to be 00:12:46.56900:12:46.579 epsilon times a over D epsilon sub 00:12:50.47000:12:50.480 naught is the permittivity of free space 00:12:52.90000:12:52.910 is eight point eight five times 10 to 00:12:56.76900:12:56.779 the minus 12 00:12:59.40000:12:59.410 Kalume squared to our Newton per square 00:13:03.06900:13:03.079 meter so make sure you know that value 00:13:06.19000:13:06.200 because you're going to use it a lot 00:13:11.35000:13:11.360 now the other epsilon without the zero 00:13:16.40000:13:16.410 is simply the permittivity of the 00:13:18.92000:13:18.930 material between the two parallel plates 00:13:23.43900:13:23.449 now epsilon is equal to K times epsilon 00:13:28.28000:13:28.290 sub not so therefore we have this 00:13:31.87900:13:31.889 equation C is equal to K times epsilon 00:13:35.26900:13:35.279 sub naught times a over D that is if you 00:13:39.59000:13:39.600 replace epsilon with K epsilon sub 00:13:42.76900:13:42.779 naught so this equation is the 00:13:47.19900:13:47.209 capacitance of a capacitor if there's 00:13:50.32900:13:50.33900:13:53.21000:13:53.220 if you have a dielectric then the 00:13:56.36000:13:56.370 capacitance can be calculated using that 00:13:59.56900:13:59.579 equation now let's talk about how to 00:14:02.78000:14:02.790 derive the formula for capacitor so 00:14:10.25000:14:10.260 let's draw the picture of a capacitor 00:14:12.25900:14:12.269 here are the two metal plates one of the 00:14:15.47000:14:15.480 plates is going to have a positive 00:14:16.51900:14:16.529 charge and the other plate is going to 00:14:19.63900:14:19.649 be negatively charged and so there's 00:14:24.05000:14:24.060 going to be an electric field that flows 00:14:26.30000:14:26.310 from the positive plate and points 00:14:28.81900:14:28.829 towards the negative plate and these two 00:14:32.62900:14:32.639 plates are separated by a distance D now 00:14:36.47000:14:36.480 you can calculate the electric field if 00:14:38.09000:14:38.100 you know the voltage across the 00:14:39.76900:14:39.779 capacitor and if you know the distance 00:14:41.87000:14:41.880 between the two plates the electric 00:14:43.69900:14:43.709 field is simply the voltage divided by 00:14:46.34000:14:46.350 the separation distance now the electric 00:14:50.24000:14:50.250 field is also equal to the surface 00:14:53.18000:14:53.190 charge density Sigma divided by epsilon 00:14:55.91000:14:55.920 sub nought and the surface charge 00:14:59.05900:14:59.069 density is basically the total charge on 00:15:02.68900:15:02.699 that plate divided by the area of the 00:15:05.68900:15:05.699 plate 00:15:09.47000:15:09.480 so starting with the equation Q equals 00:15:11.81000:15:11.820 ceiling our goal is to solve for C so C 00:15:15.02000:15:15.030 is Q divided by V and rearranged in this 00:15:21.02000:15:21.030 equation if we multiply both sides by a 00:15:23.18000:15:23.190 we can see that Q is equal to that does 00:15:27.71000:15:27.720 not look like a Q q is equal to the 00:15:30.59000:15:30.600 surface charge density Sigma times the 00:15:32.93000:15:32.940 area so let's replace Q with Sigma times 00:15:36.32000:15:36.330 a now using this equation if we solve 00:15:41.00000:15:41.010 for voltage the voltage is equal to the 00:15:44.12000:15:44.130 electric field times the separation 00:15:46.13000:15:46.140 distance so it's e times the D now using 00:15:51.68000:15:51.690 the equation in the middle if we solve 00:15:53.87000:15:53.880 for Sigma Sigma the surface charge 00:15:57.02000:15:57.030 density is equal to electric field times 00:15:59.60000:15:59.610 the permittivity of free space so let's 00:16:04.04000:16:04.050 replace it with that so e times epsilon 00:16:09.20000:16:09.210 sub naught times a divided by e o times 00:16:13.55000:16:13.560 D is equal to the capacitance so now we 00:16:16.43000:16:16.440 can cancel scene so therefore the 00:16:19.82000:16:19.830 capacitance depends on the area and the 00:16:22.73000:16:22.740 separation distance so that's how you 00:16:25.55000:16:25.560 can derive the equation now how does the 00:16:28.85000:16:28.860 capacitor work how does the battery 00:16:31.79000:16:31.800 charge a capacitor well let's draw a 00:16:34.31000:16:34.320 picture so let's draw the two metal 00:16:36.89000:16:36.900 plates of a capacitor and let's 00:16:40.22000:16:40.230 connected to a battery this is the 00:16:42.50000:16:42.510 circuit diagram of a battery the long 00:16:45.14000:16:45.150 side of a battery is the positive 00:16:46.79000:16:46.800 terminal the short side is the negative 00:16:48.80000:16:48.810 terminal so this is negative and this 00:16:54.38000:16:54.390 side is positive now before you connect 00:16:56.96000:16:56.970 the battery if the capacitor is 00:16:58.94000:16:58.950 discharged it's going to have a voltage 00:17:01.40000:17:01.410 of zero and let's connect it to a 00:17:04.55000:17:04.560 12-volt battery once you connect it 00:17:09.04000:17:09.050 there's a difference in potential 00:17:11.29000:17:11.300 whenever you have a difference in 00:17:13.32900:17:13.339 electric potential the voltage is not 00:17:17.72000:17:17.730 zero current is going to flow 00:17:21.63000:17:21.640 if the voltage is zero then no electric 00:17:25.31900:17:25.329 current will flow one way you can think 00:17:29.13000:17:29.140 about this is let's say if you have a 00:17:32.01000:17:32.020 level surface and if you have water on 00:17:35.03900:17:35.049 this surface this water will not flow 00:17:37.88000:17:37.890 the height between position a and 00:17:41.21000:17:41.220 position B is the same however let's say 00:17:45.45000:17:45.460 if you increase the angle let's say if 00:17:49.04900:17:49.059 you put it on an incline let's say a is 00:17:52.91900:17:52.929 at a higher position in B then water is 00:17:55.79900:17:55.809 going to flow from the high position to 00:17:59.01000:17:59.020 the low position and the more you 00:18:02.28000:18:02.290 increase the angle the greater the 00:18:04.74000:18:04.750 velocity it's going to water is going to 00:18:06.65900:18:06.669 flow down with more acceleration with 00:18:08.78900:18:08.799 normal force the same is true with 00:18:10.62000:18:10.630 voltage if the voltage is zero between 00:18:15.41900:18:15.429 two points that is if the electric 00:18:17.03900:18:17.049 potential zero between two points no 00:18:19.28900:18:19.299 current will flow current flows from a 00:18:22.23000:18:22.240 high electric potential to a low 00:18:25.14000:18:25.150 electric potential the same way as water 00:18:28.14000:18:28.150 flows from a high position to a low 00:18:29.82000:18:29.830 position so while the capacitor have a 00:18:33.27000:18:33.280 voltage of zero current is going to flow 00:18:36.78000:18:36.790 in a circuit now initially before we 00:18:44.97000:18:44.980 connect the battery at T equals zero the 00:18:48.90000:18:48.910 charge on the two plates is zero the 00:18:53.49000:18:53.500 number of electrons and protons are 00:18:55.11000:18:55.120 equal now let's say that on the first 00:18:57.63000:18:57.640 plate there's about a thousand electrons 00:18:59.90900:18:59.919 which means that there's a thousand 00:19:01.86000:19:01.870 protons for it to be neutral in reality 00:19:04.26000:19:04.270 is probably much more than that you have 00:19:05.58000:19:05.590 like billions and billions of electrons 00:19:07.16900:19:07.179 and protons but let's keep it simple so 00:19:12.39000:19:12.400 we have a thousand electrons and a 00:19:13.86000:19:13.870 thousand protons and on the other side 00:19:16.56000:19:16.570 we also have a thousand electrons and 00:19:19.02000:19:19.030 the thousand protons now in the metal 00:19:21.81000:19:21.820 the protons they don't move with the 00:19:24.00000:19:24.010 electrons they're free to move so keep 00:19:26.52000:19:26.530 that in mind now once you attach the 00:19:29.90900:19:29.919 battery to the capacitor which the 00:19:33.29900:19:33.309 capacitor has a voltage of zero 00:19:35.60000:19:35.610 because there's a difference in electric 00:19:38.49000:19:38.500 potential current will flow now mind you 00:19:42.37900:19:42.389 current doesn't flow in between the two 00:19:44.94000:19:44.950 metal plates of the capacitor because 00:19:46.91900:19:46.929 you haven't insulated there and 00:19:48.49900:19:48.509 insulators do not conduct electricity 00:19:50.89900:19:50.909 conductors conduct electricity so the 00:19:55.28900:19:55.299 electrons they will flow from one side 00:19:58.32000:19:58.330 to the other side now because this side 00:20:00.74900:20:00.759 has a positive charge the electrons on 00:20:03.33000:20:03.340 the Left will flow in that direction and 00:20:07.70000:20:07.710 they will continue to flow on the other 00:20:10.04900:20:10.059 side so basically what the battery does 00:20:12.37900:20:12.389 using its voltage which you can think of 00:20:15.81000:20:15.820 as an electromotive force it basically 00:20:18.29900:20:18.309 pumps electrons from one side of the 00:20:21.74900:20:21.759 capacitor to the other side and that's 00:20:24.29900:20:24.309 how it charges it so over time let me 00:20:28.88900:20:28.899 draw a new picture let's say if 200 00:20:32.99900:20:33.009 electrons travel from one plate to the 00:20:36.50900:20:36.519 other plate let's see what the situation 00:20:40.98000:20:40.990 will be so if the plate on the Left 00:20:44.54900:20:44.559 loses 200 electrons and now has 800 it 00:20:47.58000:20:47.590 started with a thousand but it has 800 00:20:49.49000:20:49.500 now the number of protons is still the 00:20:52.49900:20:52.509 same it's a thousand the plate on the 00:20:56.07000:20:56.080 right gained 200 electrons so now it has 00:20:58.56000:20:58.570 1200 but the protons are still the same 00:21:01.74000:21:01.750 the protons don't move inside a metal 00:21:06.88900:21:06.899 now if you notice the left side has a 00:21:10.52900:21:10.539 positive charge because it has 200 more 00:21:14.03900:21:14.049 protons and electrons and the right side 00:21:16.49900:21:16.509 now has a negative charge it has 200 00:21:19.68000:21:19.690 more electrons and protons so the 00:21:23.10000:21:23.110 magnitude of the charges on these two 00:21:25.47000:21:25.480 plates are equal but the sign is 00:21:28.20000:21:28.210 opposite so on the left side the charge 00:21:31.44000:21:31.450 is positive q is 200 more protons and 00:21:34.40900:21:34.419 electrons on the right side the charge 00:21:36.65900:21:36.669 is negative q is 200 more electrons and 00:21:39.72000:21:39.730 protons so the charges on these two 00:21:42.06000:21:42.070 plates will always be the same it's just 00:21:44.22000:21:44.230 that the magnitude is different 00:21:47.23000:21:47.240 now over time the capacitor will be 00:21:50.33000:21:50.340 charged to a voltage that's equal to the 00:21:53.81000:21:53.820 voltage of the battery so let's say at 00:21:56.69000:21:56.700 12 volts it has the charge of 200 now 00:22:01.22000:22:01.230 200 electrons doesn't correspond to 200 00:22:03.50000:22:03.510 coulombs but let's just say the charge 00:22:05.18000:22:05.190 is 200 just to keep things simple 00:22:07.78000:22:07.790 how much more charge can we store if we 00:22:12.23000:22:12.240 double the voltage if we double the 00:22:15.86000:22:15.870 voltage then we can store 400 units of 00:22:20.27000:22:20.280 charge as opposed to 200 units if we 00:22:23.54000:22:23.550 triple the voltage we can store 600 the 00:22:27.50000:22:27.510 capacitance is basically the ratio 00:22:29.60000:22:29.610 between how much charge within store and 00:22:34.69000:22:34.700 divided by the voltage level at that 00:22:38.36000:22:38.370 point so if you were to divide 12 by 200 00:22:43.04000:22:43.050 it's going to be equal to 12 over 400 00:22:46.13000:22:46.140 you're going to get the same value and 00:22:48.26000:22:48.270 that value actually I did it the other 00:22:51.23000:22:51.240 way around 00:22:51.91000:22:51.920 it's supposed to be charged over a 00:22:54.05000:22:54.060 voltage so if we divide 200 by 12 it's 00:22:58.40000:22:58.410 going to be equal to 400 over 24 and 00:23:01.49000:23:01.500 that ratio between the amount of charge 00:23:04.58000:23:04.590 that can be stored at a given voltage 00:23:07.39000:23:07.400 that's equal to the capacitance of the 00:23:11.06000:23:11.070 capacitor just keep in mind though this 00:23:13.58000:23:13.590 is not includes that's just the 00:23:16.55000:23:16.560 difference in electrons and protons and 00:23:18.82000:23:18.830 the allottee to calculate C you need to 00:23:22.22000:23:22.230 find a charge in coulombs and then 00:23:24.95000:23:24.960 divided by voltage to do that it's going 00:23:28.10000:23:28.110 to be n times e so basically if you have 00:23:32.69000:23:32.700 200 electrons multiplied by 1 point 6 00:23:35.21000:23:35.220 times 10 to the negative 19 and then you 00:23:38.03000:23:38.040 can get the charge Q each electron has 00:23:43.99000:23:44.000 discharged 00:23:50.75000:23:50.760 so just to review a battery charges a 00:23:55.02000:23:55.030 capacitor by pumping electrons from one 00:23:57.72000:23:57.730 side of the capacitor to the other side 00:24:00.33000:24:00.340 now once the capacitor is charged what's 00:24:04.92000:24:04.930 going to happen if we remove the battery 00:24:06.78000:24:06.790 and connect it to something that can 00:24:09.39000:24:09.400 absorb energy let's say a light bulb now 00:24:11.97000:24:11.980 let's say the capacitor has enough 00:24:14.19000:24:14.200 energy to light up the light bulb what's 00:24:16.59000:24:16.600 going to happen so let's redraw the 00:24:19.68000:24:19.690 picture that we have so this plate is 00:24:21.15000:24:21.160 positive and the other plate is negative 00:24:25.19000:24:25.200 now both plates still have about a 00:24:27.48000:24:27.490 thousand protons but the plate on the 00:24:29.91000:24:29.920 right has 1200 electrons and the one on 00:24:33.15000:24:33.160 the left is electron deficient as 800 00:24:36.30000:24:36.310 electrons so even though the plate is 00:24:39.06000:24:39.070 positively charged and less it doesn't 00:24:41.07000:24:41.080 mean that it doesn't contain electrons 00:24:42.54000:24:42.550 it simply means that there are more 00:24:44.88000:24:44.890 protons than electrons that's why it's 00:24:46.71000:24:46.720 positively charged and the plate on the 00:24:49.17000:24:49.180 right because it's negatively charged it 00:24:51.33000:24:51.340 doesn't mean that doesn't have any 00:24:52.74000:24:52.750 protons it simply means that there's 00:24:55.11000:24:55.120 more electrons than protons so when 00:24:58.80000:24:58.810 you're dealing with electric charge 00:25:00.11000:25:00.120 think of it as the difference between 00:25:02.40000:25:02.410 the number of protons and electrons 00:25:04.35000:25:04.360 because all matter contains protons and 00:25:06.96000:25:06.970 electrons now electrons are going to 00:25:10.44000:25:10.450 flow from the negatively charged plate 00:25:12.77000:25:12.780 towards the positively charged plate and 00:25:15.57000:25:15.580 that's how a capacitor discharges itself 00:25:17.55000:25:17.560 that's how it uses up its energy 00:25:20.75000:25:20.760 electrons are naturally attracted to 00:25:23.01000:25:23.020 protons so if one side is negatively 00:25:26.37000:25:26.380 charged the excess electrons will flow 00:25:28.80000:25:28.810 towards the side that is electron 00:25:31.29000:25:31.300 deficient or that has a positive charge 00:25:32.73000:25:32.740 and as these electrons flow through the 00:25:36.27000:25:36.280 wires and through the light bulb the 00:25:38.61000:25:38.620 light bulb is going to light up provide 00:25:40.44000:25:40.450 it at this capacitor has enough energy 00:25:42.12000:25:42.130 to get the job done and so that's how 00:25:44.79000:25:44.800 capacitor discharge itself now the 00:25:48.51000:25:48.520 capacitor will stop and work in when the 00:25:51.75000:25:51.760 number of electrons are equal in both 00:25:53.22000:25:53.230 sides 00:25:54.17000:25:54.180 so once 200 electrons flow through the 00:25:58.17000:25:58.180 light bulb this will now be a thousand 00:26:01.13900:26:01.149 and this will increase by 200 so it's 00:26:04.04900:26:04.059 gonna be a thousand now at that point 00:26:06.64900:26:06.659 the two plates are initialized they no 00:26:10.68000:26:10.690 longer have a charge they have equal 00:26:13.10900:26:13.119 numbers of protons electrons so the 00:26:15.95900:26:15.969 charge number plate is no longer 00:26:17.94000:26:17.950 positive human- q but rather QE is going 00:26:21.59900:26:21.609 to be equal to zero since the number of 00:26:26.39900:26:26.409 electrons are the same and the protons 00:26:28.70900:26:28.719 are the same so once it reaches the 00:26:31.25900:26:31.269 state of equilibrium that the pastor is 00:26:33.02900:26:33.039 basically dead is discharged now there 00:26:37.46900:26:37.479 are some other equations that you need 00:26:38.72900:26:38.739 to know before we begin doing some 00:26:40.56000:26:40.570 problems and that is the electric 00:26:43.04900:26:43.059 potential energy stored in the capacitor 00:26:45.08900:26:45.099 there's three equations that you need to 00:26:46.85900:26:46.869 know the first one is one-half QV 00:26:49.56000:26:49.570 it's half of the charge times the 00:26:52.88900:26:52.899 voltage now we know that Q is equal to C 00:26:56.31000:26:56.320 V so if we replace Q with CV we can get 00:27:04.37900:27:04.389 another equation the electric potential 00:27:07.13900:27:07.149 energy stored in a capacitor is also 00:27:10.44000:27:10.450 equal to one-half CV squared so make 00:27:13.85900:27:13.869 sure you know these two equations 00:27:15.06000:27:15.070 one-half QV and one-half CV squared now 00:27:19.25900:27:19.269 there's also another one because we can 00:27:23.66900:27:23.679 replace V with Q divided by C if you 00:27:29.19000:27:29.200 rearrange this equation so instead of 00:27:32.48900:27:32.499 replacing Q let's replace V now so it's 00:27:35.43000:27:35.440 going to be one-half times Q times Q 00:27:39.59900:27:39.609 over C so this equals Q squared divided 00:27:44.90900:27:44.919 by Q C so those are the three equations 00:27:49.52900:27:49.539 that you need to know to calculate the 00:27:51.35900:27:51.369 potential energy stored in a capacitor 00:27:56.45000:27:56.460 now sometimes you may need to calculate 00:27:58.73900:27:58.749 the energy density stored in a capacitor 00:28:02.29900:28:02.309 so capital u represents the potential 00:28:05.60900:28:05.619 energy I'm going to write PE and 00:28:08.24900:28:08.259 lowercase U is the energy density is 00:28:10.82900:28:10.839 basically the potential energy divided 00:28:13.28900:28:13.299 by the 00:28:14.29900:28:14.309 not the voltage but the volume so how 00:28:21.70900:28:21.719 can we derive an equation for this the 00:28:25.12900:28:25.139 electric potential energy is one-half CV 00:28:28.19000:28:28.200 squared the volume of would stay a 00:28:31.66900:28:31.679 rectangle is the last times width times 00:28:34.58000:28:34.590 height the units for volume is cubic 00:28:38.11900:28:38.129 meters the unit for energy is joules so 00:28:44.98900:28:44.999 the energy density is going to be joules 00:28:46.82000:28:46.830 per cubic meter now see let's say if we 00:28:53.41900:28:53.429 have a capacitor that doesn't have a 00:28:55.66900:28:55.679 dielectric it's going to be epsilon sub 00:28:57.79900:28:57.809 nought times a divided by D and I wrote 00:29:02.35900:29:02.369 Q this is supposed to be a squared so 00:29:05.57000:29:05.580 let me go ahead and fix that that's 00:29:07.99900:29:08.009 supposed to be a 2 and not a 3 so what 00:29:14.62900:29:14.639 do you think when you do next 00:29:17.22900:29:17.239 now we still have a V squared and last 00:29:24.79900:29:24.809 times width is basically the area we can 00:29:27.44000:29:27.450 think of the height as a distance now V 00:29:31.15900:29:31.169 it is basically the electric field times 00:29:33.20000:29:33.210 the distance that is the distance 00:29:35.62900:29:35.639 between the two plates so we can replace 00:29:42.07900:29:42.089 V squared with a d squared so we can 00:29:47.89900:29:47.909 cancel D and we can cancel a so now what 00:29:53.18000:29:53.190 we have left over is 1/2 epsilon sub 00:29:56.41900:29:56.429 naught e squared 00:29:58.39900:29:58.409 we still have 1 D value left over and 00:30:01.54900:30:01.559 there's a D on the bottom so those can 00:30:04.09900:30:04.109 be canceled as well so therefore the 00:30:07.54900:30:07.559 energy density which is represented by 00:30:10.90900:30:10.919 lowercase U is one-half epsilon sub 00:30:13.60900:30:13.619 naught times the square of the electric 00:30:15.25900:30:15.269 field so the energy density stored in a 00:30:19.33900:30:19.349 capacitor is dependent on the electric 00:30:21.04900:30:21.059 field so just some things to know 00:30:24.99000:30:25.000 number one a metal contains one point 00:30:27.91000:30:27.920 five times ten to fourteen access 00:30:30.64000:30:30.650 electronics what is the charge of this 00:30:33.13000:30:33.140 metal in microphones well Q is equal to 00:30:37.78000:30:37.790 n times e so let's find Q and this 00:30:45.43000:30:45.440 represents the number of electrons 00:30:47.76000:30:47.770 that's one point five times ten to the 00:30:50.26000:30:50.270 14 excess electrons and E is the charge 00:30:54.34000:30:54.350 per electron 00:31:03.24000:31:03.250 so E is 1.6 times 10 to negative 19 00:31:06.74000:31:06.750 coulombs per electron so the number of 00:31:12.12000:31:12.130 electrons will cancel and then when we 00:31:14.15900:31:14.169 multiply these two values the units will 00:31:16.64900:31:16.659 be in Coombes so you should get two 00:31:29.43000:31:29.440 point four times ten to negative five 00:31:33.35000:31:33.360 kaloumes and it's negative now we want 00:31:37.26000:31:37.270 to find the charge in micro clones so 00:31:39.87000:31:39.880 let's convert it one micro Coulomb is 00:31:42.89900:31:42.909 basically 1 times 10 to the minus 6 00:31:45.18000:31:45.190 coulombs so these units will cancel so 00:31:53.18000:31:53.190 the final answer is negative 24 micro 00:31:57.51000:31:57.520 clubs number two a metal sphere contains 00:32:03.36000:32:03.370 a charge of 17 micro Coulomb 00:32:05.76000:32:05.770 if there are nine point six times ten to 00:32:08.88000:32:08.890 the 14 protons on the sphere how many 00:32:12.00000:32:12.010 electrons are there 00:32:13.49000:32:13.500 well let's convert microcoulombs into 00:32:17.07000:32:17.080 the number of protons since the charge 00:32:20.03900:32:20.049 is positive this means that there's more 00:32:22.47000:32:22.480 protons than electrons 1 times 10 to 00:32:29.78900:32:29.799 minus 6 is equal to 1 micro Coulomb and 00:32:36.79900:32:36.809 one proton has a charge of 1 point 6 00:32:41.65900:32:41.669 times 10 to negative 19 coulombs so 00:32:46.89000:32:46.900 notice that the net microcoulombs will 00:32:49.20000:32:49.210 cancel and the unit kaloumes will cancer 00:33:02.24000:33:02.250 so you should get 4.37 five times ten to 00:33:10.23000:33:10.240 the 14 protons now keep in mind this is 00:33:15.02900:33:15.039 the amount of excess protons not the 00:33:20.64000:33:20.650 total number of protons so what this 00:33:23.90900:33:23.919 move is that there's four point three 00:33:25.98000:33:25.990 seven five times ten to the 14 more 00:33:29.03900:33:29.049 protons than electrons now we already 00:33:32.43000:33:32.440 have the total number of protons it's 00:33:34.74000:33:34.750 nine point six times ten to the 14 if we 00:33:37.89000:33:37.900 subtract that number by this number we 00:33:41.73000:33:41.740 can get the number of electrons so it's 00:33:44.31000:33:44.320 nine point six times ten to the 14 minus 00:33:48.12000:33:48.130 four point three seven five times 10 to 00:33:52.16900:33:52.179 the 14 and that's going to give us how 00:33:55.11000:33:55.120 many electrons are present on this year 00:34:03.74000:34:03.750 so the answer is 5 point 2 2 5 times 10 00:34:09.51000:34:09.520 to the 14 electrons so because we have 00:34:14.22000:34:14.230 more protons than electrons that's why 00:34:18.54000:34:18.550 the net charge is positive but it 00:34:22.88900:34:22.899 doesn't mean that there is no electrons 00:34:24.35900:34:24.369 so keep that in mind number three a tiny 00:34:31.13900:34:31.149 dust particle contains 8500 electrons 00:34:34.02000:34:34.030 and 8470 protons what is the net charge 00:34:38.07000:34:38.080 on this particle so what should we do in 00:34:42.06000:34:42.070 the problem you need to keep reliant is 00:34:44.34000:34:44.350 the difference between electrons and 00:34:46.80000:34:46.810 protons that's important that's needed 00:34:49.40900:34:49.419 to calculate a charge so here's an 00:34:53.66900:34:53.679 equation that you can use Q is going to 00:34:55.23000:34:55.240 equal the difference between the number 00:34:59.16000:34:59.170 of protons and minus electrons times one 00:35:02.60900:35:02.619 point six times 10 to the negative 19 00:35:07.81000:35:07.820 so this 8470 protons and 8500 electrons 00:35:14.77000:35:14.780 if we subtract those two numbers it's 00:35:18.11000:35:18.120 going to give us negative 30 and we want 00:35:21.95000:35:21.960 it to be negative because there's more 00:35:23.27000:35:23.280 electrons and protons and so the total 00:35:25.58000:35:25.590 charge has to be negative 00:35:32.65000:35:32.660 so the final answer is simply negative 00:35:35.12000:35:35.130 30 times 1.6 times 10 to the negative 19 00:35:39.58000:35:39.590 so the total charge is negative four 00:35:42.71000:35:42.720 point eight times 10 to the negative 18 00:35:46.36000:35:46.370 Kalume number four how much charge can 00:35:56.24000:35:56.250 be stored on a 100 micro farad capacitor 00:35:59.65000:35:59.660 when placed across a 12 volt battery to 00:36:03.28000:36:03.290 calculate the charge Q is equal to cv 00:36:07.42000:36:07.430 the capacitance C is 100 micro farad so 00:36:12.17000:36:12.180 that's 100 times 10 to minus 6 farad's 00:36:15.94000:36:15.950 the voltage across the capacitor is 12 00:36:19.46000:36:19.470 volts so if we multiply these two it's 00:36:26.33000:36:26.340 going to give us 1.2 times 10 to minus 00:36:32.84000:36:32.850 string kaloumes so that's how much 00:36:37.40000:36:37.410 charge that can be stored on this 00:36:40.70000:36:40.710 capacitor now how much energy is stored 00:36:44.90000:36:44.910 in this capacitor so we can use the 00:36:47.42000:36:47.430 equation knew the potential energy is 00:36:50.72000:36:50.730 equal to one-half CV squared C is 100 00:36:57.38000:36:57.390 times 10 to the minus 6 and the voltage 00:37:00.38000:37:00.390 is 12 00:37:09.74000:37:09.750 so this is equal to seven point two 00:37:13.77000:37:13.780 times ten to minus three jewels and 00:37:18.53000:37:18.540 that's it 00:37:25.22000:37:25.230 number five a capacitor is connected 00:37:28.09900:37:28.109 across a hundred volt power source and 00:37:30.71000:37:30.720 that's 2.5 joules of energy stored in it 00:37:33.73000:37:33.740 how much electric charge is stored in 00:37:36.85900:37:36.869 the capacitor so make sure you pause the 00:37:40.67000:37:40.680 video as you work on these problems the 00:37:43.67000:37:43.680 equation that we'll need is this one the 00:37:45.68000:37:45.690 electric potential energy is one-half Q 00:37:47.75000:37:47.760 times V and we have the energy stored 00:37:50.66000:37:50.670 it's 2.5 joules and we're looking for Q 00:37:58.90000:37:58.910 the voltage is 100 half of 100 is 50 so 00:38:07.25000:38:07.260 2.5 divided by 50 is point zero five so 00:38:13.60900:38:13.619 this capacitor has point zero five 00:38:15.85900:38:15.869 kaloumes of charge stored in it now what 00:38:19.94000:38:19.950 about Part B what is the capacitance in 00:38:23.48000:38:23.490 micro farad capacitance is the ratio 00:38:26.96000:38:26.970 between the charge and the voltage so we 00:38:30.53000:38:30.540 have point zero five coulombs divided by 00:38:33.38000:38:33.390 100 volts so that's equal to five times 00:38:39.92000:38:39.930 10 to minus 4 farad's now is converting 00:38:44.00000:38:44.010 to micro farad's 1 micro farad is 1 00:38:53.83900:38:53.849 times 10 to the minus 6 so we got to 00:38:58.13000:38:58.140 divide the two numbers 00:39:03.45000:39:03.460 so this is equal to five hundred 00:39:06.51000:39:06.520 microfarads 00:39:15.12000:39:15.130 number six a hundred Klum's of charge is 00:39:18.63000:39:18.640 stored when twenty volts is applied 00:39:20.00900:39:20.019 across capacitor what voltage is 00:39:22.92000:39:22.930 required to store 300 grams of charge 00:39:25.96900:39:25.979 we know that the capacitance depends on 00:39:29.84900:39:29.859 the area and the distance between the 00:39:31.65000:39:31.660 plates it doesn't depend on the charge 00:39:36.02900:39:36.039 or the voltage but it is the ratio 00:39:37.55900:39:37.569 between the charge and the voltage so if 00:39:41.24900:39:41.259 you change the voltage let's say if you 00:39:43.85900:39:43.869 increase the voltage of the battery the 00:39:45.98900:39:45.999 capacitance remain the same increase in 00:39:49.01900:39:49.029 the voltage will affect the charge from 00:39:51.15000:39:51.160 out the capacitance Q 1 over V 1 is 00:39:54.45000:39:54.460 equal to C if we change Q and V let's 00:39:58.46900:39:58.479 say Q 2 and V 2 it would still equal to 00:40:01.14000:40:01.150 the same capacitance therefore Q 1 over 00:40:05.03900:40:05.049 V 1 is equal to Q 2 over V 2 so that's 00:40:09.32900:40:09.339 the equation that we're going to use now 00:40:11.69000:40:11.700 let's consider Part A the charge 00:40:15.12000:40:15.130 increased from 100 Klum's to 300 Klum's 00:40:19.27900:40:19.289 so if we increase the charge by a factor 00:40:22.04900:40:22.059 of 3 what effect will have on the 00:40:25.04900:40:25.059 voltage if Q increases then Z will 00:40:29.75900:40:29.769 increase proportionally so the voltage 00:40:32.18000:40:32.190 must increase by a factor of 3 it has to 00:40:35.91000:40:35.920 be 60 volts using the equation you're 00:40:38.88000:40:38.890 going to get the same answer and let's 00:40:40.92000:40:40.930 say Q 1 is 100 Klum's V 1 is 20 volts Q 00:40:46.07900:40:46.089 2 is 300 and we'll look at 4 V 2 let's 00:40:49.31900:40:49.329 cross multiply a hundred times V 2 is 00:40:52.01900:40:52.029 just 100 is e to 20 times 300 2 times 3 00:40:58.95000:40:58.960 is 6 and then add the three zeros that's 00:41:01.76900:41:01.779 going to be six thousand six thousand 00:41:05.57900:41:05.589 divided by 100 is 60 all you need to do 00:41:10.89000:41:10.900 is cancel 2 zeros so V 2 is 60 now what 00:41:17.70000:41:17.710 about Part B how much charge can be 00:41:21.45000:41:21.460 stored 00:41:23.66000:41:23.670 if 150 volts is applied well let's use a 00:41:31.76000:41:31.770 film equation let's keep to month as 100 00:41:35.03000:41:35.040 Coons and v1 is still going to be 20 so 00:41:39.53000:41:39.540 v2 is now 150 and let's solve for Q 2 so 00:41:44.05900:41:44.069 let's cross multiply so we're going to 00:41:46.97000:41:46.980 have 20 Q 2 is equal to 100 times 150 00:41:55.18000:41:55.190 and that's about a 15000 so now we got 00:42:02.90000:42:02.910 to divide both sides by 20 so 15,000 00:42:06.74000:42:06.750 divided by 20 is 750 so 750 combs of 00:42:12.28900:42:12.299 charge will be stored if we increase the 00:42:15.44000:42:15.450 voltage to 150 so as you increase the 00:42:19.64000:42:19.650 voltage across the capacitor more 00:42:22.57900:42:22.589 electric charge can be stored and the 00:42:25.57900:42:25.589 ratio between how much charge you can 00:42:28.22000:42:28.230 store at that given voltage can be used 00:42:32.42000:42:32.430 to calculate the capacitance so if we 00:42:34.73000:42:34.740 want to find the capacitance here's what 00:42:37.76000:42:37.770 we can do we can take the q1 value which 00:42:42.04900:42:42.059 is 100 and divided by 20 that's going to 00:42:45.58900:42:45.599 be five coulombs per volt so that's five 00:42:49.03000:42:49.040 farad's or we could take the voltage at 00:42:53.63000:42:53.640 300 clothes at 300 Klum's the voltage is 00:42:58.78000:42:58.790 6300 divided by 60 is also 5 so you get 00:43:02.56900:43:02.579 the same constant so we're dealing with 00:43:06.23000:43:06.240 a 5 farad capacitor number 7 a capacitor 00:43:10.81900:43:10.829 is made of two square metal plates with 00:43:13.73000:43:13.740 side lengths 3 centimeters separated by 00:43:15.62000:43:15.630 distance of 1 millimeter with air in 00:43:18.62000:43:18.630 between the plates so let's draw a 00:43:20.53900:43:20.549 picture so let's say this is the first 00:43:24.28900:43:24.299 square metal plate and here's the second 00:43:26.75000:43:26.760 one so the side lengths are 3 00:43:30.55900:43:30.569 centimeters by 3 centimeters and the 00:43:33.10900:43:33.119 distance between the two plates 00:43:36.33000:43:36.340 is only one millimeter how can we 00:43:40.93000:43:40.940 calculate the capacitance and we have 00:43:43.21000:43:43.220 error in between to find it we can use 00:43:48.64000:43:48.650 this equation C is equal to epsilon sub 00:43:51.19000:43:51.200 naught times a over D epsilon sub naught 00:43:55.51000:43:55.520 is eight point eight five times ten to 00:43:58.78000:43:58.790 minus twelve the area the area of the 00:44:02.65000:44:02.660 squares length times width three 00:44:04.69000:44:04.700 centimeters by three centimeters but you 00:44:06.28000:44:06.290 need to convert that to meters so it's 00:44:08.95000:44:08.960 point zero three meters times point zero 00:44:11.85900:44:11.869 three meters or you can simply square it 00:44:15.00000:44:15.010 the distance is one millimeter and milli 00:44:18.52000:44:18.530 is ten to minus three so it's one times 00:44:21.49000:44:21.500 ten to the negative three meters 00:44:34.77000:44:34.780 so you should get seven point nine six 00:44:39.94000:44:39.950 five times ten to the negative twelve 00:44:42.66000:44:42.670 thirds now a picofarad is 10 to minus 12 00:44:47.11000:44:47.120 ferrets so you can round it in safe 00:44:49.93000:44:49.940 about 8.0 Pico farad's Part B what is 00:45:00.31000:45:00.320 the new capacitance if an insulator with 00:45:02.89000:45:02.900 a dielectric constant of four is added 00:45:05.65000:45:05.660 in between the plates so let's put an 00:45:08.50000:45:08.510 insulator in between it what's going to 00:45:10.42000:45:10.430 happen anytime you add an insulator the 00:45:14.53000:45:14.540 dielectric constant will increase I mean 00:45:16.36000:45:16.370 the K value will increase and so C is 00:45:18.88000:45:18.890 going to increase unfortunately and the 00:45:20.77000:45:20.780 voltage will decrease so see the new 00:45:24.67000:45:24.680 capacitance is equal to K times the 00:45:27.88000:45:27.890 original capacitance and K is four so 00:45:30.61000:45:30.620 it's going to be four times eight 00:45:32.44000:45:32.450 picofarads so now it's going to be 32 00:45:35.43000:45:35.440 Pico farad's now what about the voltage 00:45:41.97000:45:41.980 the voltage is going to decrease but the 00:45:44.41000:45:44.420 equation that you need is this one Z is 00:45:47.20000:45:47.210 going to be equal to the original 00:45:48.16000:45:48.170 voltage divided by K the original 00:45:51.37000:45:51.380 voltage is 100 and K is 4 so 100 divided 00:45:56.38000:45:56.390 by 4 that's a V by the way is 25 so 00:46:02.20000:46:02.210 that's going to be the new voltage 25 00:46:04.87000:46:04.880 volts number 8 a capacitor has two 00:46:09.49000:46:09.500 parallel plates separated by 2 00:46:12.01000:46:12.020 millimeters and is connected across a 50 00:46:15.28000:46:15.290 volt battery Part A what is the electric 00:46:19.03000:46:19.040 field between the plates so if you want 00:46:21.76000:46:21.770 to draw a picture here's what we have 00:46:24.03000:46:24.040 so here is a 2 plates of the capacitor 00:46:28.11000:46:28.120 one side is positive and the other side 00:46:33.10000:46:33.110 is negative 00:46:39.34000:46:39.350 and here's the electric field in between 00:46:41.48000:46:41.490 two plates to calculate the electric 00:46:43.79000:46:43.800 field all you need is the voltage across 00:46:46.91000:46:46.920 the capacitor and the separation 00:46:48.92000:46:48.930 distance so it's V over D the voltage is 00:46:53.75000:46:53.760 50 volts and the distance has to be in 00:46:56.66000:46:56.670 meters two millimeters is basically 2 00:46:59.83000:46:59.840 times 10 to minus 3 meters so 50 divided 00:47:06.02000:47:06.030 by point zero zero two is 25 thousand so 00:47:11.30000:47:11.310 the electric field is 25 thousand volts 00:47:15.11000:47:15.120 per meter or you can use the units in 00:47:18.41000:47:18.420 Newton's per Coulomb now what about Part 00:47:22.52000:47:22.530 B what is the surface charge density the 00:47:27.17000:47:27.180 surface charge density is the product of 00:47:30.41000:47:30.420 the electric field times the 00:47:32.18000:47:32.190 permittivity of free space you've seen 00:47:35.72000:47:35.730 this equation earlier in the video he is 00:47:38.15000:47:38.160 equal to a sigma divided by epsilon sub 00:47:41.78000:47:41.790 naught so solving for Sigma the surface 00:47:45.17000:47:45.180 charge density it's a times epsilon sub 00:47:47.96000:47:47.970 naught so it's 25,000 times eight point 00:47:54.89000:47:54.900 eight five times 10 to minus 12 and this 00:48:03.23000:48:03.240 is going to give you two point two one 00:48:05.95000:48:05.960 times ten to the minus seven kaloumes 00:48:09.77000:48:09.780 per square meter Part C 00:48:17.75000:48:17.760 how much charge is stored on each plate 00:48:21.08900:48:21.099 if the area is point 1 square meters 00:48:24.79900:48:24.809 well we know that Sigma the surface 00:48:27.59900:48:27.609 charge density is Q divided by 8 Q is 00:48:31.71000:48:31.720 the electric charge measured includes a 00:48:33.63000:48:33.640 is the area in square meters so that's 00:48:37.10900:48:37.119 why Sigma is Coulomb's per square meter 00:48:39.34900:48:39.359 so we could find the charge by 00:48:42.08900:48:42.099 multiplying the surface charge density 00:48:43.52000:48:43.530 by the area so Q is equal to Sigma which 00:48:48.93000:48:48.940 is 2 point 2 1 times 10 to minus 7 00:48:53.49000:48:53.500 kaloumes per square meter and the area 00:48:57.66000:48:57.670 is 0.1 square meters so these units will 00:49:03.83900:49:03.849 cancel giving us the desired you're 00:49:06.05900:49:06.069 going to include so 2.2 one times 10 to 00:49:09.72000:49:09.730 the minus 7 times point one it's just 00:49:12.21000:49:12.220 going to be two point two one times 10 00:49:15.99000:49:16.000 to the negative eight it's going to be 00:49:17.37000:49:17.380 smaller so that's the electric charge 00:49:20.40000:49:20.410 stored in this capacitor 00:49:23.05900:49:23.069 now what about Part D calculate the 00:49:26.01000:49:26.020 capacitance let's do it two ways C is 00:49:30.39000:49:30.400 equal to Q divided by V the charge is 00:49:34.53000:49:34.540 2.2 1 times 10 to the minus 8 the 00:49:38.88000:49:38.890 voltage is 50 volts 00:49:46.15000:49:46.160 and so this is going to be four point 00:49:49.56900:49:49.579 four two times 10 to negative 10 Farage 00:49:56.57900:49:56.589 now let's calculate it using the other 00:49:58.99000:49:59.000 equation so let's use this one C is 00:50:05.58900:50:05.599 equal to epsilon sub naught times a 00:50:08.62000:50:08.630 divided by D so it's eight point eight 00:50:11.92000:50:11.930 five times 10 to negative twelve the 00:50:16.21000:50:16.220 area is point one square meters and the 00:50:19.48000:50:19.490 distance to millimeters is point zero 00:50:22.26900:50:22.279 zero two meters so this will also give 00:50:31.35900:50:31.369 you four point four two it's really 4.45 00:50:35.07900:50:35.089 but this answer is around an answer 00:50:38.78900:50:38.799 times 10 to negative ten 00:50:41.33900:50:41.349 ference so using either equation will 00:50:45.09900:50:45.109 give you the same answer and that was 00:50:47.68000:50:47.690 moving on to Part II how much energy is 00:50:53.68000:50:53.690 stored in this capacitor so there's a 00:50:57.06900:50:57.079 lot of equations that we can use so 00:51:00.13000:51:00.140 let's go ahead and use this equation U 00:51:02.74000:51:02.750 is equal to Q squared divided by its you 00:51:06.19000:51:06.200 see we've used the other forms so let's 00:51:08.95000:51:08.960 use a different form of the equation so 00:51:12.81900:51:12.829 Q the electric charge is two point two 00:51:18.99900:51:19.009 one times ten to the negative eight 00:51:21.02900:51:21.039 kaloumes that's what we got in Part C 00:51:26.30900:51:26.319 divided by two times the capacitance 00:51:30.26900:51:30.279 which is a four point four to five times 00:51:35.04900:51:35.059 10 to the negative 10 00:51:48.06900:51:48.079 so this is equal to five point five two 00:51:51.87000:51:51.880 times ten to negative seven joules 00:52:00.51000:52:00.520 now the last thing that we need to do is 00:52:02.40000:52:02.410 calculate the energy density the energy 00:52:05.28000:52:05.290 density lowercase U is one-half epsilon 00:52:09.48000:52:09.490 sub naught times e squared so it's 1/2 00:52:13.26000:52:13.270 times the permittivity of free space 00:52:15.47000:52:15.480 which is eight point eight five times 00:52:17.79000:52:17.800 ten to the minus twelve times the square 00:52:21.03000:52:21.040 of the electric field and the electric 00:52:22.89000:52:22.900 field we found it to be twenty-five 00:52:24.54000:52:24.550 thousand volts from you 00:52:36.42000:52:36.430 so this is equal to two point seven 00:52:40.57000:52:40.580 seven times ten to negative three and 00:52:43.89000:52:43.900 it's energy per unit volume so it's 00:52:47.11000:52:47.120 joules per cubic meter and that's it so 00:52:51.49000:52:51.500 that's it for this video this is just a 00:52:53.14000:52:53.150 basic introduction to capacitors and 00:52:56.16000:52:56.170 thanks for watching
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