WEBVTT 00:00.360 --> 00:06.200 Today, let's dive into one of the most important building blocks of electronics, which is capacitors. 00:06.960 --> 00:11.760 We encounter capacitors everywhere from computers to smartphones, and understanding them deeply will 00:11.760 --> 00:15.760 help you become much more confident when designing and analyzing circuits. 00:16.040 --> 00:18.400 So what exactly is a capacitor? 00:18.640 --> 00:25.720 A capacitor is a component that stores energy in the form of an electric field created by accumulated 00:25.720 --> 00:34.160 electric charge on two conductive plates, separated by an insulating material. 00:34.280 --> 00:38.400 In simpler words, think of a capacitor like a small energy tank. 00:38.440 --> 00:44.960 It fills up the electric charge and can be released when it's needed. 00:45.680 --> 00:52.600 Now, when you first connect the capacitor into a circuit, something interesting happens. 00:53.080 --> 01:03.260 Current initially flows into it very easily, current very easily, and almost like it's just a piece 01:03.260 --> 01:03.780 of wire. 01:04.340 --> 01:05.340 But here's the key. 01:05.580 --> 01:13.660 Now, instead of letting that current pass straight through, the capacitor gradually builds up electrical 01:13.660 --> 01:15.260 charge on its plates. 01:16.020 --> 01:25.060 As the charge builds, electrical field forms between the plates and this electric field starts resisting 01:25.260 --> 01:27.420 more current flowing in. 01:28.140 --> 01:31.740 That's why the current naturally decreases over time. 01:32.380 --> 01:36.060 Now, in short, at the beginning it is easy. 01:36.860 --> 01:40.980 Over time it is harder and harder to current to flow. 01:41.140 --> 01:47.460 And when the capacitor is fully charged, current almost stops. 01:48.220 --> 01:55.380 Now, since it takes time for this electrical field to build up, capacitors are extremely useful when 01:55.380 --> 01:58.980 we want to smooth out sudden changes in voltage. 01:59.340 --> 02:02.760 Now, for example, if there's a sudden surge in a current. 02:02.800 --> 02:11.520 The capacitor absorbs some of that surge, and if the current suddenly drops, the capacitor releases 02:11.520 --> 02:15.720 its stored charge to keep the voltage steady. 02:15.760 --> 02:22.240 Now, this property is crucial in digital circuits, where the sudden voltage spikes could otherwise 02:22.240 --> 02:25.880 cause errors and burn components. 02:26.640 --> 02:29.000 Now let's get a bit mathematical here. 02:29.280 --> 02:30.400 I don't like that. 02:30.400 --> 02:33.480 But don't worry, I will walk you through slowly. 02:33.920 --> 02:38.000 So the voltage across the capacitor changes with time. 02:38.440 --> 02:43.720 Now we can describe this equation with this v time. 02:44.560 --> 02:47.200 Now let's break it down very carefully. 02:47.880 --> 02:56.360 Now v here means the voltage across the capacitor at the specific time. 02:56.560 --> 03:07.170 Now this is what time this I t here is the current Flowing into the capacitor at any moment. 03:07.850 --> 03:14.730 And the see here is the capacitance value measured in farads. 03:15.450 --> 03:25.090 And this symbol, called integral, simply means adding up very tiny contributions of current over time. 03:25.850 --> 03:34.650 Now, if you're not familiar with the calculus, imagine filling a bucket with tiny drops of water. 03:34.690 --> 03:43.730 Here, every small amount of current flowing in adds a drop of voltage to the capacitor over time. 03:44.210 --> 03:49.690 If those drops add up, the voltage builds up. 03:50.570 --> 03:58.370 Now, the important idea here is the more current that flows into the capacitor, the more voltage it 03:58.410 --> 03:59.210 develops. 04:00.010 --> 04:02.810 But it happens gradually. 04:04.710 --> 04:05.630 Gradually. 04:05.990 --> 04:07.550 Not like instantly. 04:07.550 --> 04:07.950 Here. 04:08.750 --> 04:09.390 Like this. 04:10.190 --> 04:11.790 It happens gradually. 04:12.390 --> 04:15.870 And now let's look at a real example to make all this more concrete. 04:16.510 --> 04:27.750 This simple circuit has five volts of power supply, a switch, a one kilo ohm resistor and one farad 04:27.950 --> 04:28.870 capacitor. 04:29.150 --> 04:34.110 Now, when the switch is first closed, here's a story that unfolds here. 04:34.510 --> 04:40.790 At the very beginning we have t which equals to zero. 04:41.510 --> 04:44.310 Now the capacitor here is completely empty. 04:44.550 --> 04:46.270 It behaves like a var. 04:47.030 --> 04:52.270 Now the full five volts appears across the resistor. 04:52.630 --> 04:57.070 If the circuit is closed, let's close the circuit and see what will happen. 04:59.870 --> 05:05.570 The full 5.0V appears Here's across the resistor. 05:06.370 --> 05:14.890 The voltage across the capacitor, which is what v b c is zero volts. 05:15.250 --> 05:16.890 The current is maximum. 05:17.530 --> 05:23.090 And the initial current calculation you will learn here is I. 05:23.210 --> 05:27.450 Here is initial 5.0V. 05:28.210 --> 05:35.970 One kilo ohms equals what 5.0mA. 05:36.690 --> 05:37.650 Now this is simple. 05:37.690 --> 05:46.010 Ohm's law here which you learned in previous lecture which is current equals voltage divided by resistance. 05:46.650 --> 05:55.730 And as the time passes, the capacitor starts building up charge voltage across the capacitor V BC starts 05:55.770 --> 06:06.910 rising as the time goes on and the voltage across the resistor start dropping, which is what v a p 06:07.630 --> 06:18.590 v a b is not stopping voltage, a to B starts dropping and the current is gradually decreases. 06:19.390 --> 06:22.870 The energy flow follows this important rule here. 06:23.230 --> 06:36.070 5.0V initial time multiplied by r v and b c here b c and time. 06:36.710 --> 06:45.670 Now this, uh, formula here just says the battery voltage must always be shared between the resistor 06:45.670 --> 06:47.030 and the capacitor. 06:47.750 --> 06:56.030 And eventually, if we had enough time to come into the steady state, the capacitor voltage reaches 06:56.710 --> 07:08.730 5.0V and the resistor voltage, which is five volts, and the resistor voltage drops to zero and almost 07:08.970 --> 07:11.570 no current falls to nearly zero. 07:11.610 --> 07:13.370 Not to zero, but nearly zero. 07:14.690 --> 07:16.570 Maybe 0.01 and zero point. 07:16.570 --> 07:21.770 Because we have extra component here and takes it takes energy and capacitor. 07:21.970 --> 07:28.370 Capacitors are not 100% efficient here and that's why we have this current. 07:29.050 --> 07:33.050 Now at first the circuit behaves like it's just a resistor here. 07:33.770 --> 07:39.690 Over time, the capacitor charges up stealing voltage from the resistor. 07:39.930 --> 07:46.770 And until it finally blocks and the current flows completely without any problem. 07:47.490 --> 07:54.410 And now what you're seeing here is this is basically a voltage and the time graph of this capacitor 07:54.570 --> 07:56.050 on our circuit here. 07:56.690 --> 08:00.810 Now let's take a closer look and a deeper look on this figure. 08:01.530 --> 08:04.370 Now this graph is more than just lines. 08:04.410 --> 08:15.740 Now it just tells the full story of how capacitor behaves on the left y axis, which shows the voltage 08:15.740 --> 08:32.900 across the capacitor v b c v b c on the right y axis shows the voltage across the resistor v a c no 08:32.940 --> 08:34.500 v a b here. 08:35.220 --> 08:37.500 Now the scales are opposite. 08:37.740 --> 08:42.540 As one voltage rises, the other falls. 08:43.340 --> 08:47.540 Now the current is at its maximum value. 08:48.420 --> 08:52.980 So how we basically draw that we will use a different color. 08:54.180 --> 08:54.860 So what. 08:55.500 --> 08:58.500 It will go up to the one volt. 08:58.740 --> 09:06.260 And over there just stay there or maybe write it more curved. 09:06.460 --> 09:06.860 Yeah. 09:07.680 --> 09:08.440 No it will. 09:08.600 --> 09:10.440 On the fourth millisecond. 09:11.240 --> 09:16.640 And yes, that's basically how our voltage graph behaves. 09:17.400 --> 09:21.440 So at t0 t is a time. 09:21.720 --> 09:31.640 By the way t0 v BC is zero volts because the capacitor has no charge here. 09:32.360 --> 09:34.160 We have just started our circuit. 09:34.160 --> 09:34.640 Right. 09:35.800 --> 09:38.520 Let's also let's also close our switch. 09:39.200 --> 09:49.960 And yeah in the VAB the a b is five volts because the full supply voltage is across. 09:49.960 --> 09:55.320 The resistor current is at its maximum value. 09:56.160 --> 10:03.600 The voltage VB across the capacitor increases exponentially. 10:04.400 --> 10:07.940 The voltage V a b across the resistor. 10:08.300 --> 10:10.700 Decrease exponentially. 10:10.700 --> 10:12.580 So this is basically how it is. 10:13.460 --> 10:15.220 Also we will use this color. 10:15.940 --> 10:22.940 As I said this is what this is a opposite scale graph. 10:23.380 --> 10:26.380 This is another graph which is VBC and VAB. 10:27.140 --> 10:32.940 So y exponential you may ask here in the beginning the capacitor charges quickly because there is a 10:32.940 --> 10:36.500 large voltage difference pushing the current. 10:36.940 --> 10:46.580 So 5.0V is a lot bigger than 0.0V or 0.0. 5V or 3V. 10:46.580 --> 10:47.020 Right. 10:47.460 --> 10:53.420 But 5.0V is not bigger than 4.8V, for example. 10:53.460 --> 10:53.940 Right? 10:55.020 --> 11:01.660 So in the beginning, the capacitor charges quickly because there is a large voltage difference pushing 11:01.700 --> 11:02.900 the current up. 11:03.580 --> 11:13.880 As the capacitor fills up, the voltage difference gets smaller and smaller and the and the charging 11:14.120 --> 11:17.240 slows down, but not stops. 11:17.240 --> 11:21.440 Remember, capacitors are not 100% efficient. 11:22.200 --> 11:30.200 This slowing down is characteristics of exponential behavior and the voltage across the capacitor at 11:30.200 --> 11:49.080 any time t is v bc time v eight multiplied by one minus minus t r c where v eight. 11:49.120 --> 11:53.800 Here is a supply voltage of 5.0V. 11:54.480 --> 12:06.400 In this case, the e here is the base of the natural logarithm approximately 4.71 and r c. 12:06.440 --> 12:09.340 Here is the time constant. 12:10.060 --> 12:17.500 So at one time constant, which is one time constant, is basically one millisecond. 12:18.220 --> 12:30.020 So it is after the one millisecond, the capacitor has charged up to 63% of its final voltage. 12:31.220 --> 12:40.780 And at six time constant six time constants, we have what we have approximately five volts. 12:41.100 --> 12:43.940 And and how we get this five volts. 12:44.460 --> 12:58.740 So in this case t is 6.0 milliseconds and v eight is basically five volts E t is basically again same 12:58.780 --> 13:00.740 6.0 milliseconds. 13:01.700 --> 13:13.630 And yeah use we will get approximately 5.0V Probably less than 5.0V. 13:14.350 --> 13:20.270 Meanwhile, the voltage across the resistor A B drops in the opposite manner. 13:20.750 --> 13:23.430 It starts with 5.0V. 13:24.070 --> 13:28.150 So remember capacitor starts where it starts with 0.0V. 13:28.150 --> 13:32.030 But resistor starts from 5.0V. 13:32.030 --> 13:37.110 Because the power source is 5.0V it's giving 5.0V to resistor. 13:37.830 --> 13:48.150 And yeah it starts with 5.0V and it falls exponentially to zero volts, almost zero volts as the capacitor 13:48.310 --> 13:49.470 charges up. 13:50.150 --> 13:58.990 And the key insight for you is the capacitor and resistor trade voltage like they are giving each other 13:59.230 --> 13:59.990 voltage. 14:00.750 --> 14:03.430 This is resistor this capacitor and. 14:03.470 --> 14:03.870 Yeah. 14:04.030 --> 14:12.330 And the faster the trade which is faster trade means smaller RC the faster the circuit responds, and 14:12.330 --> 14:22.290 after about five six time constants, the circuit reaches a steady state and summary. 14:22.450 --> 14:30.730 Key points for you is capacitors charge gradually and resist instant changes. 14:31.490 --> 14:43.570 Current starts high and falls to near zero as the capacitor fills up and the time constant r c predicts 14:43.570 --> 14:46.770 how quickly the capacitor changes. 14:47.530 --> 14:48.690 And this is the formula. 14:50.050 --> 14:51.770 And after the after about. 14:51.810 --> 15:00.130 In this case, after about five six milliseconds or five six time constants, the capacitor is almost 15:00.130 --> 15:07.050 fully charged and the capacitor stores energy as an electric field, not as a continuous current. 15:07.530 --> 15:09.090 Now that's it for our lecture. 15:09.090 --> 15:11.610 Thank you for watching and I'm waiting you in the next lecture.