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Capacitors (7 of 9) Energy Stored in a Capacitor, An Explanation

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Language: en

00:00:01.820
okay into video as you can see we are
00:00:04.460 00:00:04.470 going to go over a discussion and talk
00:00:06.829 00:00:06.839 about how to calculate how energy is
00:00:09.740 00:00:09.750 stored and the amount of energy that is
00:00:11.930 00:00:11.940 stored in a capacitor all right now this
00:00:15.110 00:00:15.120 is a general diagram 1/2 of a capacitor
00:00:17.450 00:00:17.460 and when we talk about energy stored in
00:00:20.570 00:00:20.580 a capacitor we usually you can say two
00:00:23.269 00:00:23.279 different ways you can say that charge
00:00:26.210 00:00:26.220 is stored so a capacitor store charge
00:00:29.000 00:00:29.010 but in order to store charge the battery
00:00:31.999 00:00:32.009 has to do work to move the charges from
00:00:34.250 00:00:34.260 one plate to another so really when
00:00:36.979 00:00:36.989 you're storing charge the battery is
00:00:39.770 00:00:39.780 doing work and therefore what you're
00:00:42.229 00:00:42.239 really storing is energy and that energy
00:00:44.299 00:00:44.309 can be released at a later time okay
00:00:47.750 00:00:47.760 so what we like to say that the energy
00:00:49.760 00:00:49.770 stored is equal to the work done by the
00:00:53.779 00:00:53.789 battery to move the charges from one
00:00:55.369 00:00:55.379 plate to another so what the battery
00:00:57.439 00:00:57.449 does is it takes the charges the
00:01:00.470 00:01:00.480 electrons the negative charges move them
00:01:02.900 00:01:02.910 from one plate to the other plate when
00:01:05.390 00:01:05.400 it does that it has to do work it just
00:01:08.570 00:01:08.580 like when you have gravitational
00:01:09.830 00:01:09.840 potential energy when you do work you
00:01:12.260 00:01:12.270 store gravitate when you do work you
00:01:14.240 00:01:14.250 store gravitational potential energy but
00:01:16.609 00:01:16.619 in this case we're not storing
00:01:17.570 00:01:17.580 gravitational potential energy or
00:01:19.580 00:01:19.590 storing electric potential energy so the
00:01:22.640 00:01:22.650 energy stored the potential energy store
00:01:24.679 00:01:24.689 is equal to the work done by the battery
00:01:26.240 00:01:26.250 and that energy we like to say is stored
00:01:30.530 00:01:30.540 in the electric field between the plates
00:01:32.480 00:01:32.490 so when all of the charges have been
00:01:34.280 00:01:34.290 moved over we have a positive plate and
00:01:36.950 00:01:36.960 a negative plate and we have an electric
00:01:38.929 00:01:38.939 field that goes from the positive to
00:01:41.030 00:01:41.040 negative and the energy is stored in the
00:01:45.649 00:01:45.659 put in the electric field between those
00:01:47.780 00:01:47.790 plates
00:01:48.319 00:01:48.329 okay so stored energy stored charge work
00:01:53.740 00:01:53.750 potential energy the energy is stored in
00:01:56.480 00:01:56.490 electric field between the plates okay
00:01:59.270 00:01:59.280 now let's just look at a little bit more
00:02:00.560 00:02:00.570 detail how we calculate that how we
00:02:03.950 00:02:03.960 calculate the work done or really we
00:02:05.929 00:02:05.939 talk about the amount of energy that's
00:02:07.370 00:02:07.380 been stored moving the charges from one
00:02:09.770 00:02:09.780 plate to another
00:02:11.150 00:02:11.160 you know this is the equation that we
00:02:13.910 00:02:13.920 used previously to calculate the amount
00:02:17.690 00:02:17.700 of work it takes to move a charge to a
00:02:20.870 00:02:20.880 certain potential difference as I
00:02:23.000 00:02:23.010 mentioned earlier when you do work you
00:02:25.070 00:02:25.080 store energy in this case an electric
00:02:26.960 00:02:26.970 potential energy so in order to store
00:02:29.420 00:02:29.430 that energy the battery has to work or
00:02:31.790 00:02:31.800 when the battery does work it's going to
00:02:33.620 00:02:33.630 store electric potential energy through
00:02:36.740 00:02:36.750 the movement okay of those electrons
00:02:40.220 00:02:40.230 with the moving of charge all right now
00:02:43.100 00:02:43.110 what we're going to do is you can see
00:02:44.870 00:02:44.880 here we have a 9-volt battery we have a
00:02:47.240 00:02:47.250 switch and this is kind of schematic the
00:02:49.220 00:02:49.230 capacity to parallel plates for the
00:02:50.870 00:02:50.880 capacitor and we're going to take one
00:02:53.390 00:02:53.400 unit of charge which is Q which is your
00:02:57.110 00:02:57.120 electron and we're going to move that
00:02:58.490 00:02:58.500 from one plate to another okay so I
00:03:01.970 00:03:01.980 close the switch and right when I close
00:03:04.820 00:03:04.830 the switch to charge and start to move
00:03:06.470 00:03:06.480 from one plate to another and we're
00:03:08.150 00:03:08.160 going to kind of look at this one
00:03:09.610 00:03:09.620 electron at a time till the first
00:03:12.530 00:03:12.540 electron gets moved from one plate
00:03:16.900 00:03:16.910 through the battery and to the other
00:03:20.030 00:03:20.040 plate and what we do is now we're going
00:03:22.400 00:03:22.410 to use this equation amount of work done
00:03:25.010 00:03:25.020 is equal to Q two charge through the
00:03:29.330 00:03:29.340 potential difference to which that
00:03:30.890 00:03:30.900 charge has moved okay we're going to do
00:03:32.990 00:03:33.000 that right down here for the first
00:03:34.550 00:03:34.560 electron if the work is equal to the
00:03:38.390 00:03:38.400 amount of charge the charge dollars at
00:03:39.620 00:03:39.630 one point six times ten to minus
00:03:40.820 00:03:40.830 nineteen coulombs now the question is in
00:03:43.550 00:03:43.560 this case is what potential difference
00:03:45.830 00:03:45.840 was that charge move through well you
00:03:48.770 00:03:48.780 notice we have a nine volt battery and
00:03:50.300 00:03:50.310 right when we close the switch the
00:03:51.560 00:03:51.570 charges start to move but the very first
00:03:54.949 00:03:54.959 electronic think of its electron per
00:03:56.930 00:03:56.940 electron the very first electron when
00:03:59.060 00:03:59.070 the very first electrons move from one
00:04:00.920 00:04:00.930 plate to the other when it's moved not
00:04:03.410 00:04:03.420 before but when it's moved there's no
00:04:06.199 00:04:06.209 potential difference between those
00:04:07.460 00:04:07.470 00:04:07.970 00:04:07.980 so we have charge we have no potential
00:04:09.980 00:04:09.990 difference so down here it's work is
00:04:11.420 00:04:11.430 equal to the charge times the potential
00:04:13.730 00:04:13.740 difference through which that charge was
00:04:15.530 00:04:15.540 moveable that charge was moved through
00:04:17.539 00:04:17.549 no potential difference so the work it
00:04:20.090 00:04:20.100 takes to move the first electron is
00:04:22.340 00:04:22.350 really zero you
00:04:24.440 00:04:24.450 rules of work zero joules of work is
00:04:27.410 00:04:27.420 done to move the first electron alright
00:04:30.890 00:04:30.900 now the next thing we have of course now
00:04:33.140 00:04:33.150 we have a positive plate and negative
00:04:35.300 00:04:35.310 plate and we're going to continue to do
00:04:37.340 00:04:37.350 that move the electrons over link of it
00:04:40.100 00:04:40.110 like currently moving them over one at a
00:04:41.750 00:04:41.760 time one of the times that does happen
00:04:43.340 00:04:43.350 one at a time but you can kind of think
00:04:45.380 00:04:45.390 of it like that until we have almost all
00:04:47.360 00:04:47.370 of the electrons have been moved over so
00:04:50.600 00:04:50.610 this plate is almost fully charged this
00:04:53.000 00:04:53.010 plays almost fully charge the capacitor
00:04:54.740 00:04:54.750 is only four almost fully charged but we
00:04:56.810 00:04:56.820 have one last electronically going need
00:04:59.510 00:04:59.520 to move the data you can move one more
00:05:02.240 00:05:02.250 electrons we're going to move that last
00:05:03.770 00:05:03.780 electron over like that now the plates
00:05:07.580 00:05:07.590 are fully charged and no more electrons
00:05:09.800 00:05:09.810 are going from one side or from one
00:05:11.960 00:05:11.970 plate to the other now let's calculate
00:05:13.930 00:05:13.940 the amount of take work it takes to move
00:05:16.730 00:05:16.740 that very last electron using this same
00:05:20.300 00:05:20.310 equation now we have it we're doing this
00:05:22.250 00:05:22.260 kind of electron by electron okay the
00:05:26.030 00:05:26.040 amount of work is equal to the charge Q
00:05:28.340 00:05:28.350 times the potential - what's the
00:05:30.230 00:05:30.240 potential difference this time well
00:05:31.250 00:05:31.260 really when we move the last electron
00:05:33.910 00:05:33.920 the capacitor is basically almost
00:05:36.770 00:05:36.780 basically fully charged so there's nine
00:05:38.900 00:05:38.910 volts across the capacitor so that
00:05:41.560 00:05:41.570 electron is moved through a potential
00:05:43.940 00:05:43.950 difference of nine volts so we're now
00:05:46.130 00:05:46.140 going to multiply that by nine one point
00:05:47.750 00:05:47.760 six times ten to minus nineteen times
00:05:49.910 00:05:49.920 nine volts is equal to one point four
00:05:52.850 00:05:52.860 times ten to the minus 18 joules of
00:05:56.030 00:05:56.040 energy now this over here is zero that's
00:05:58.580 00:05:58.590 the work it took the energy that was
00:06:00.650 00:06:00.660 stored to move the first electron this
00:06:03.170 00:06:03.180 is the energy or the work it took to
00:06:05.320 00:06:05.330 move the last electron or the energy
00:06:08.210 00:06:08.220 stored now what we could do is we could
00:06:10.490 00:06:10.500 add all those up and summon up because
00:06:13.970 00:06:13.980 the first one is zero which we
00:06:15.740 00:06:15.750 calculated then the next one moves to a
00:06:18.050 00:06:18.060 little potential difference so it's a
00:06:19.460 00:06:19.470 little bit more than zero
00:06:20.720 00:06:20.730 and the next one's a little bit more and
00:06:22.610 00:06:22.620 more and more and more until the last
00:06:24.350 00:06:24.360 one this is the work it takes to move
00:06:26.420 00:06:26.430 the last one I'm going to add them all
00:06:27.770 00:06:27.780 up but you could kind of see we have the
00:06:30.560 00:06:30.570 zero and the maximum amount and then the
00:06:34.190 00:06:34.200 work is actually equal to one-half
00:06:37.640 00:06:37.650 the total amount of charge that's moved
00:06:40.230 00:06:40.240 and the potential difference through
00:06:42.540 00:06:42.550 which is moved okay so you can think of
00:06:45.390 00:06:45.400 the whole amount of charges moved and to
00:06:47.790 00:06:47.800 move through nine bolts okay so now you
00:06:50.880 00:06:50.890 can see we have Q this is Q and this is
00:06:53.760 00:06:53.770 Q we change it from this using rhythms
00:06:55.410 00:06:55.420 capital Q and this is the potential
00:06:58.170 00:06:58.180 difference to which it moves so the work
00:06:59.520 00:06:59.530 done the energy store is equal to
00:07:01.340 00:07:01.350 one-half times Q can it be all right now
00:07:06.090 00:07:06.100 you this is the same equation we have in
00:07:07.680 00:07:07.690 the previous page you often see this
00:07:10.050 00:07:10.060 equation written three different ways
00:07:11.850 00:07:11.860 because this is W work is equal to
00:07:13.740 00:07:13.750 one-half Q times V the charge and a
00:07:17.270 00:07:17.280 potential difference we just move but
00:07:19.680 00:07:19.690 you remember we had this equation we
00:07:21.330 00:07:21.340 like to call the capacitor equation Q
00:07:23.010 00:07:23.020 equal C times V now I can take this
00:07:26.100 00:07:26.110 equation Q and substitute it in here for
00:07:29.070 00:07:29.080 this Q so I'm going to substitute CV the
00:07:33.390 00:07:33.400 capacitance of the capacitor and the
00:07:35.190 00:07:35.200 voltage across the capacitor in here for
00:07:39.690 00:07:39.700 this Q and then I get that W the work
00:07:42.660 00:07:42.670 done or the energy store is equal to 1/2
00:07:44.940 00:07:44.950 C this is this C and I had an extra V so
00:07:48.450 00:07:48.460 it's V squared at the voltage squared
00:07:50.690 00:07:50.700 one-half CV squared now I can also in
00:07:54.840 00:07:54.850 this equation I can rearrange this
00:07:56.610 00:07:56.620 equation solve it for the voltage okay
00:08:00.930 00:08:00.940 the voltage is equal to the charge
00:08:02.940 00:08:02.950 divided by the capacitance I can also
00:08:05.040 00:08:05.050 substitute that in here
00:08:06.390 00:08:06.400 and then you'll see we have Q squared
00:08:08.130 00:08:08.140 over C so this is another form of that
00:08:10.080 00:08:10.090 same equation the work the energy stored
00:08:13.680 00:08:13.690 is equal to one-half Q squared over C
00:08:17.240 00:08:17.250 okay so that's the three ways of three
00:08:20.160 00:08:20.170 different ways you will see this
00:08:21.360 00:08:21.370 equation written once when you know the
00:08:23.790 00:08:23.800 voltage and the charge went we know the
00:08:25.740 00:08:25.750 boulders and the capacitance and once
00:08:27.120 00:08:27.130 for another charge in the contestant
00:08:28.640 00:08:28.650 okay so there you go that's a brief
00:08:30.750 00:08:30.760 introduction and explanation as to how
00:08:33.630 00:08:33.640 energy is stored in a capacitor and how
00:08:36.659 00:08:36.669 much energy is stored or how much work
00:08:38.219 00:08:38.229 is done to move those charges or store
00:08:41.100 00:08:41.110 that energy okay in the next video we'll
00:08:43.350 00:08:43.360 do a couple simple calculations you move
00:08:45.600 00:08:45.610 that video up in the upper right hand
00:08:47.070 00:08:47.080 corner of this video thank you very much
00:08:49.410 00:08:49.420 watching hooks on the help please do all
00:08:51.030 00:08:51.040 the following three
00:08:52.080 00:08:52.090 subscribe to my channel give all my
00:08:53.850 00:08:53.860 excellent figures chemistry and math
00:08:55.680 00:08:55.690 videos please write down their below
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00:09:01.560 00:09:01.570 nice problem comment the comments I can
00:09:02.820 00:09:02.830 load thank you very much for watching
00:09:04.140 00:09:04.150 we'll see you in the next video

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