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How To Calculate The Energy Stored In a Capacitor

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Language: en

00:00:00.079
in this video we're gonna focus on
00:00:03.110 00:00:03.120 calculating the energy stored in a
00:00:05.809 00:00:05.819 capacitor so how much energy can be
00:00:08.750 00:00:08.760 stored if 10 volts is applied to a 5
00:00:12.049 00:00:12.059 farad capacitor so let's talk about what
00:00:16.039 00:00:16.049 values that we have so we have the
00:00:18.950 00:00:18.960 capacitance which is equal to C and
00:00:21.730 00:00:21.740 that's five ferret's and we also have
00:00:26.029 00:00:26.039 the voltage which is 10 volts what
00:00:30.140 00:00:30.150 formula do we need to calculate the
00:00:31.730 00:00:31.740 potential energy stored in this
00:00:33.590 00:00:33.600 capacitor the form that we need is this
00:00:36.410 00:00:36.420 one it's one-half CV squared so it's
00:00:40.790 00:00:40.800 going to be one half multiplied by the
00:00:43.130 00:00:43.140 capacitor which is the capacitance it's
00:00:45.619 00:00:45.629 five ferrets and the voltage is 10 volts
00:00:51.279 00:00:51.289 half of five is two point five and ten
00:00:54.560 00:00:54.570 squared is a hundred so this is going to
00:00:57.139 00:00:57.149 be 250 joules of potential energy now if
00:01:04.070 00:01:04.080 this energy can be released in point
00:01:06.770 00:01:06.780 zero one seconds what is the power
00:01:09.440 00:01:09.450 exerted by the capacitor during this
00:01:12.320 00:01:12.330 time so how can we calculate the power
00:01:16.030 00:01:16.040 power is the rate at which energy is
00:01:19.130 00:01:19.140 transferred it's work divided by time
00:01:22.090 00:01:22.100 the work that's required to charge up
00:01:25.310 00:01:25.320 this capacitor to ten volts is 250
00:01:28.730 00:01:28.740 joules now let's replace W with 250
00:01:34.670 00:01:34.680 joules and the time is point zero one
00:01:38.690 00:01:38.700 seconds now one Joule per second is a
00:01:42.289 00:01:42.299 one so if we take 250 and divided by
00:01:45.260 00:01:45.270 point zero one that's equal to 25
00:01:48.530 00:01:48.540 thousand watts which is a very big
00:01:51.410 00:01:51.420 number and so even though a capacitor
00:01:54.770 00:01:54.780 may store a small amount of energy it
00:01:58.310 00:01:58.320 can store and deliver that energy in a
00:02:00.889 00:02:00.899 very short period of time and so the
00:02:03.740 00:02:03.750 power output of a capacitor can be huge
00:02:05.899 00:02:05.909 even though it doesn't last very long so
00:02:09.109 00:02:09.119 capacitor is very quick in storing and
00:02:11.809 00:02:11.819 delivering energy which
00:02:13.059 00:02:13.069 useful but it isn't stored that much
00:02:15.280 00:02:15.290 energy unless you have a very very big
00:02:16.839 00:02:16.849 capacitor and so that's it for this
00:02:19.000 00:02:19.010 problem now let's move on to number two
00:02:22.050 00:02:22.060 it takes 20 volts to store 80 kaloumes
00:02:25.809 00:02:25.819 of charge on a certain capacitor how
00:02:29.530 00:02:29.540 much potential energy is stored in this
00:02:32.229 00:02:32.239 capacitor so we have the voltage which
00:02:37.270 00:02:37.280 is 20 volts and a charge is 80 kaloumes
00:02:43.500 00:02:43.510 so how can we calculate the potential
00:02:46.330 00:02:46.340 energy with Q and V the potential energy
00:02:49.629 00:02:49.639 is one-half Q V so it's 1/2 times the
00:02:54.640 00:02:54.650 charge which is 80 kaloumes and the unit
00:02:58.750 00:02:58.760 for a volt 1 volt is one Joule per
00:03:02.500 00:03:02.510 Coulomb so volt which is electric
00:03:06.459 00:03:06.469 potential is the ratio between the
00:03:08.580 00:03:08.590 electric potential energy per unit
00:03:10.599 00:03:10.609 charge so 20 volts is basically 20
00:03:14.500 00:03:14.510 joules per galloon and so we could see
00:03:17.229 00:03:17.239 how the unit kaloumes will cancel giving
00:03:19.629 00:03:19.639 us the unit joules so half of 80 is 40
00:03:23.679 00:03:23.689 and 40 times 20 is 800 so there's 800
00:03:29.020 00:03:29.030 joules of potential energy stored in
00:03:31.240 00:03:31.250 this capacitor now let's calculate the
00:03:35.199 00:03:35.209 capacitance of this capacitor the
00:03:41.409 00:03:41.419 capacitance is the ratio between the
00:03:43.629 00:03:43.639 charge stored divided by the voltage so
00:03:47.649 00:03:47.659 we have 80 coulombs of charge divided by
00:03:50.319 00:03:50.329 20 volts and so it's 4 coulombs per volt
00:03:53.740 00:03:53.750 which is 4 farad's and so that's it for
00:03:58.689 00:03:58.699 Part B number 3 how much energy is
00:04:03.580 00:04:03.590 stored
00:04:04.119 00:04:04.129 if 500 kaloumes of charge rests on a 10
00:04:07.629 00:04:07.639 farad capacitor and what is the voltage
00:04:10.539 00:04:10.549 across this capacitor so in this problem
00:04:14.379 00:04:14.389 we have the charge which is Q that's 500
00:04:17.379 00:04:17.389 kaloumes and the capacitance is 10
00:04:20.770 00:04:20.780 ferret's so we can use this formula the
00:04:24.610 00:04:24.620 potential energy is going to be 1/2
00:04:27.030 00:04:27.040 times q squared divided by C so it's 1/2
00:04:31.870 00:04:31.880 of 500 squared divided by 10 500 squared
00:04:41.529 00:04:41.539 is 250,000 if we divide that by 10
00:04:44.740 00:04:44.750 that's 25,000 and then divide that by 2
00:04:47.370 00:04:47.380 this is gonna be 12,500 joules so that's
00:04:53.200 00:04:53.210 the potential energy stored in this
00:04:54.610 00:04:54.620 capacitor now what is the voltage across
00:04:58.029 00:04:58.039 this capacitor well we know that Q is
00:05:00.580 00:05:00.590 equal to C V so we have 500 coulombs of
00:05:04.180 00:05:04.190 charge now let's see if we can
00:05:07.390 00:05:07.400 understand it conceptually
00:05:08.680 00:05:08.690 a 10 farad capacitor means that it can
00:05:12.010 00:05:12.020 hold 10 coulombs of charge per one volt
00:05:14.800 00:05:14.810 now if we increase the voltage to 10
00:05:16.960 00:05:16.970 volts it can hold a hundred coulombs of
00:05:19.990 00:05:20.000 charge
00:05:20.500 00:05:20.510 the ratio between charge and voltage
00:05:22.990 00:05:23.000 will always be 10 and if we increase the
00:05:26.740 00:05:26.750 50 volts it can store 500 glooms of
00:05:29.680 00:05:29.690 charge and so see in this problem is 10
00:05:33.870 00:05:33.880 and we gotta solve for V so we need to
00:05:36.730 00:05:36.740 divide both sides by 10 so the voltage
00:05:41.409 00:05:41.419 is 500 Klum's divided by 10 farad's
00:05:44.230 00:05:44.240 which will be 50 volts as well sometimes
00:05:48.580 00:05:48.590 you can see it conceptually if you
00:05:50.649 00:05:50.659 understand what a fair it is so a
00:05:53.920 00:05:53.930 capacitor with one farad can store one
00:05:56.080 00:05:56.090 Coulomb of charge per one volt a 10
00:05:58.600 00:05:58.610 farad capacitor can store 10 glooms of
00:06:01.270 00:06:01.280 charge per one Vil a 200 farad capacitor
00:06:05.500 00:06:05.510 can store 200 grams of charge per 1 volt
00:06:08.740 00:06:08.750 so hopefully that makes sense number for
00:06:12.909 00:06:12.919 a certain capacitor has 25 joules of
00:06:16.240 00:06:16.250 stored potential energy when connected
00:06:19.120 00:06:19.130 across the 10 volt battery how much
00:06:21.159 00:06:21.169 energy can the capacitor store when
00:06:23.529 00:06:23.539 connected across a 20 volt battery now
00:06:27.310 00:06:27.320 we know that a potential energy is
00:06:28.689 00:06:28.699 one-half CV squared now the capacitance
00:06:34.149 00:06:34.159 of the capacitor will not change
00:06:37.350 00:06:37.360 so if we're dealing with the same
00:06:38.700 00:06:38.710 capacitor C is constant so we could say
00:06:41.460 00:06:41.470 that the potential energy is
00:06:42.809 00:06:42.819 proportional to V squared
00:06:45.649 00:06:45.659 now even though U is also equal to
00:06:48.029 00:06:48.039 one-half QV when you adjust the voltage
00:06:51.719 00:06:51.729 it affects the charge on the capacitor
00:06:53.610 00:06:53.620 so that's not constant we can't use this
00:06:56.040 00:06:56.050 formula to describe it so now that we
00:07:00.420 00:07:00.430 know that U the potential energy is
00:07:03.330 00:07:03.340 proportional to the square of the
00:07:04.800 00:07:04.810 voltage what happens if we double the
00:07:07.559 00:07:07.569 voltage well 2 squared is 4 so the
00:07:11.189 00:07:11.199 potential energy should increase by a
00:07:12.839 00:07:12.849 factor 4 so it was 25 joules
00:07:16.290 00:07:16.300 if we multiply that by 4 it should now
00:07:19.080 00:07:19.090 increase to a hundred joules so now
00:07:23.879 00:07:23.889 let's see if we can get this answer
00:07:25.230 00:07:25.240 another way
00:07:32.100 00:07:32.110 let's write a ratio between u 2 & u 1 so
00:07:35.700 00:07:35.710 u 1 is going to be 1/2 C V 1 squared u 2
00:07:40.409 00:07:40.419 is 1/2 C V 2 squared V changes so that's
00:07:44.399 00:07:44.409 why I have a subscript for that but C
00:07:45.929 00:07:45.939 doesn't change so we could say that u 2
00:07:49.170 00:07:49.180 divided by u 1 is equal to V 2 squared
00:07:52.589 00:07:52.599 over V 1 squared so the first potential
00:07:55.920 00:07:55.930 energy is 25 joules when as a voltage of
00:07:59.540 00:07:59.550 10 volts connected across it so what is
00:08:04.529 00:08:04.539 the potential energy if we increase the
00:08:06.510 00:08:06.520 voltage to 20 20 squared is 400 10
00:08:12.990 00:08:13.000 squared is 100 and so if we cross
00:08:15.990 00:08:16.000 multiply this is gonna be 25 times 400
00:08:19.589 00:08:19.599 which is 10,000 and this is going to
00:08:23.070 00:08:23.080 equal 100 times u 2 so now we get a
00:08:26.730 00:08:26.740 divide both sides by 100 10,000 divided
00:08:31.050 00:08:31.060 by 100 is 100 and so that's another way
00:08:34.649 00:08:34.659 in which you can calculate the potential
00:08:36.089 00:08:36.099 energy of a capacitor if you change the
00:08:38.819 00:08:38.829 voltage across it now let's work on our
00:08:42.630 00:08:42.640 last problem how much energy is stored
00:08:45.360 00:08:45.370 in a 150 micro farad capacitor if a 12
00:08:49.740 00:08:49.750 volt battery is connected across it now
00:08:52.949 00:08:52.959 most capacitors don't have a Radian of 1
00:08:56.579 00:08:56.589 farad or 10 farad's that's pretty high
00:08:58.500 00:08:58.510 for standard capacitor in a typical
00:09:01.350 00:09:01.360 electric circuit most capacitors are in
00:09:04.889 00:09:04.899 the micro farad range or in the nano
00:09:06.660 00:09:06.670 farad range it's rare to come across
00:09:09.750 00:09:09.760 those in the middlee farad range even
00:09:11.400 00:09:11.410 though you might see it sometimes so how
00:09:14.370 00:09:14.380 much energy is stored in this particular
00:09:15.600 00:09:15.610 capacitor so we can use this familiar
00:09:18.300 00:09:18.310 equation one-half CV squared so the
00:09:22.380 00:09:22.390 capacitance is 150 micro farad or 150
00:09:25.620 00:09:25.630 times 10 to minus 6 ferrets and the
00:09:28.560 00:09:28.570 voltage is 12 volts so you just got to
00:09:32.069 00:09:32.079 plug that in
00:09:35.970 00:09:35.980 and so the amount of potential energy
00:09:39.450 00:09:39.460 stored in this capacitor is pretty small
00:09:41.490 00:09:41.500 it's point zero one zero eight joules
00:09:47.330 00:09:47.340 now how much charge is stored in this
00:09:50.550 00:09:50.560 capacitor electric charge is equal to C
00:09:53.730 00:09:53.740 times V is the capacitance which is 150
00:09:57.420 00:09:57.430 times 10 to the minus six farad's
00:09:59.810 00:09:59.820 multiplied by the voltage of 12 volts so
00:10:09.180 00:10:09.190 this 2 is a small number it's point zero
00:10:11.820 00:10:11.830 zero one eight kaloumes and so most
00:10:16.710 00:10:16.720 capacitors that are of a standard size
00:10:21.650 00:10:21.660 usually fall around this range

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