WEBVTT 00:00.400 --> 00:01.080 All right. 00:01.120 --> 00:06.400 Now that we have covered capacitors and how they store energy in an electric field, it is time to explore 00:06.400 --> 00:09.960 their magnetic cousin, which is inductors. 00:10.720 --> 00:12.320 What is an inductor, you may ask? 00:12.840 --> 00:19.000 An inductor is a fundamental passive electronic component that stores energy in a magnetic field. 00:19.280 --> 00:27.120 This magnetic field forms whenever a current flows through the coil of wire inside the inductor. 00:27.920 --> 00:36.760 To give you a deeper analogy, if capacitors resist sudden changes in voltage, inductors resist sudden 00:36.760 --> 00:38.360 changes in current. 00:38.680 --> 00:41.880 So imagine trying to install a spin up a heavy flywheel. 00:42.040 --> 00:47.200 It resists your effort initially, but once it gets going, it keeps spinning easily. 00:47.480 --> 00:51.160 Now that's exactly how an inductor behaves toward electric current. 00:51.840 --> 00:53.520 How does an inductor behave? 00:53.560 --> 01:00.160 So when a voltage is applied to a circuit containing an inductor, initially the, the inductor strongly 01:00.160 --> 01:02.320 resists any change in current. 01:02.320 --> 01:04.680 It behaves almost like an open circuit. 01:04.920 --> 01:12.080 As time passes, the inductor builds up a magnetic field, gradually allowing more current to flow, 01:12.200 --> 01:17.800 and eventually, once the magnetic field is fully established, the inductor acts like a simple piece 01:17.800 --> 01:21.160 of wire, which is low resistance. 01:22.000 --> 01:23.720 So simple summary. 01:24.440 --> 01:29.400 At first, inductor blocks certain current. 01:29.720 --> 01:40.760 Later inductor allows current to pass, and finally inductor behaves like a short wire or DC in a steady 01:41.600 --> 01:42.280 state. 01:42.960 --> 01:48.960 Now this unique behavior is essential in controlling and smoothing electrical signals, especially in 01:49.000 --> 01:50.920 fast switching circuits. 01:51.640 --> 01:58.800 So real world example of inductors is we can say that inductors are used in computers. 01:58.800 --> 02:08.480 So if you open your computer motherboard and now near the CPU, you will see a notice donut shaped components 02:08.520 --> 02:11.000 wrapped in a copper wire. 02:11.720 --> 02:16.080 Now these are inductors that we are talking here. 02:16.400 --> 02:21.040 Now their role is to filter and smooth the voltage feeding to the CPU. 02:21.600 --> 02:27.800 Now, without them, tiny fluctuations in power could cause data corruption, crashes, or even hardware 02:27.800 --> 02:28.360 damage. 02:28.760 --> 02:34.360 Inductors are critical because they stabilize the current, preventing sudden spikes that could disrupt 02:34.400 --> 02:36.120 sensitive microprocessors. 02:36.920 --> 02:40.520 So how inductors react mathematically. 02:41.280 --> 02:42.120 You may ask? 02:42.640 --> 02:50.320 So we have formula which is basically the mathematical relationship describing an inductor is. 02:51.160 --> 02:54.120 Now let's break it down carefully here. 02:54.840 --> 02:59.000 So here As always, you will learn from the previous lectures. 02:59.040 --> 03:04.240 VTI is the instantaneous voltage across the inductor. 03:04.960 --> 03:06.120 T here is time. 03:06.120 --> 03:10.920 Remember L here is the inductance. 03:11.680 --> 03:20.840 Inductance measured in Henries or H, indicating how strongly the inductor resists changes in current. 03:21.280 --> 03:24.960 And d I t divided by d t. 03:25.000 --> 03:31.800 Here is the derivative of current with respect to time, describing how fast the current is trying to 03:31.800 --> 03:32.440 change. 03:33.120 --> 03:43.280 If we interpret this basically a fast changing current which means large, this results in a large opposing 03:43.280 --> 03:44.800 voltage across the inductor. 03:45.600 --> 03:52.440 A slow or no change in current results in little to no voltage across the inductor. 03:53.120 --> 03:58.200 In everyday language, you can say that the faster you try to change the current, the harder the inductor 03:58.200 --> 04:00.960 fights back by generating a voltage. 04:01.800 --> 04:08.880 Now this behavior protects circuits against damaging current surges, as we always do. 04:09.040 --> 04:12.080 We have explained this with a simple circuit. 04:12.280 --> 04:17.560 Now in this circuit we have a power supply five volts. 04:18.360 --> 04:20.440 Also, we have an inductor. 04:21.320 --> 04:23.520 This inductor is actually not kilohertz. 04:24.280 --> 04:27.120 This is how you describe an inductor. 04:27.840 --> 04:32.520 And we have a resistor which is one kilo ohms again. 04:33.320 --> 04:42.160 So when you close the switch here initially the inductor takes the full five voltage which basically 04:42.160 --> 04:43.600 acts like an open circuit. 04:44.320 --> 04:50.040 So no current flows through the resistor here right now. 04:51.640 --> 04:53.600 And as time goes on. 04:54.480 --> 04:59.280 Like you see here, the magnetic field builds up in this inductor. 04:59.280 --> 05:04.120 So the inductor voltage decreases, resistor voltage increases. 05:04.120 --> 05:09.640 And finally the resistor voltage gets five volts here. 05:09.640 --> 05:11.880 In this case you can see it's a BC. 05:11.920 --> 05:16.600 So B to C gets highest voltage over time. 05:17.120 --> 05:25.920 And you can see inductor resistance almost comes closer to non-zero but not fully zero here. 05:26.640 --> 05:32.400 So basically finally the resistor gets full five volts and steady current flows. 05:33.160 --> 05:38.160 And if we go to time constant we have the time here. 05:39.080 --> 05:45.600 So the time constant T tells us how quickly the current increases. 05:45.800 --> 05:54.960 And in our case if we try to calculate that At 1.01 ten. 05:55.840 --> 06:04.000 Sixth power 1.0 multiplied by ten three power ohm. 06:04.840 --> 06:11.600 You see, this is basically three because it is 1000Ω, right? 06:12.280 --> 06:25.240 And yeah, basically 1.0 ten power negative nine is 1.0 nanoseconds. 06:25.240 --> 06:25.960 We get here. 06:26.680 --> 06:37.400 So after about one nanoseconds the current has reached 63% of its final value here. 06:37.840 --> 06:38.280 Oops. 06:39.080 --> 06:39.480 Yeah. 06:39.720 --> 06:40.360 Here. 06:40.400 --> 06:42.920 Almost estimated here. 06:43.720 --> 06:47.000 So here it is 60%. 06:47.760 --> 06:52.210 And after about five six nanoseconds. 06:53.010 --> 07:03.090 It, as you can see here, almost, but not it's not ever 100% because not in electronics, there's 07:03.090 --> 07:06.370 no component that is almost 100% efficient. 07:06.850 --> 07:13.690 But we can say that it is almost 100% the current reached here. 07:15.050 --> 07:23.330 And as we calculate it here, it just needs five six nanoseconds to reach almost 100%. 07:23.530 --> 07:27.090 And after that it will go on stable. 07:27.850 --> 07:34.410 So basically we can use the inductors as stabilizers for the current. 07:35.010 --> 07:40.650 And in ultrafast circuits like CPUs, even nanoseconds. 07:40.650 --> 07:47.170 Here matters greatly considering how fast the CPUs are today. 07:48.010 --> 07:56.410 And here you can see we have a graph of our circuits, inductors, how it behaves, how it acts. 07:57.250 --> 08:03.610 So this graph shows the how the voltage or how the voltages behave over time. 08:03.610 --> 08:15.970 After closing the switch in upper circuit here in the left y axis we can see it shows the voltage of 08:16.010 --> 08:16.610 BC. 08:17.330 --> 08:28.690 So this basically means the voltage across the resistor voltage B and C, and in the right y axis it 08:28.690 --> 08:33.930 shows the voltage AB which is a b here. 08:34.610 --> 08:38.370 So it includes in voltage AB it includes inductor and voltage BC. 08:38.410 --> 08:40.090 It includes the resistor here. 08:40.770 --> 08:47.730 And x axis is basically time which is in nanoseconds. 08:48.450 --> 08:59.090 So at time zero we have zero volts which across BC because no current yet. 08:59.090 --> 09:03.210 So no voltage across the resistors and in the VAB. 09:04.330 --> 09:12.930 And if the time is zero, you can see that it is the entire power supply voltage across inductor. 09:13.690 --> 09:21.090 As the time increases, BC rises exponentially toward five volts. 09:21.770 --> 09:27.690 And the a b here falls toward zero volts. 09:27.690 --> 09:38.370 Here, because the change is fast at first, then it slows down as the circuit reaches equilibrium. 09:39.570 --> 09:42.610 So you may ask why exponential? 09:43.210 --> 09:54.050 Because a change is fast at first, then slows down as the circuit reaches top goal here and we have 09:54.050 --> 10:09.650 the voltage formula V, a, b is basically T 5.0V multiplied by one e times t. 10:10.370 --> 10:19.650 So where this e here is basically Euler's number approximately 2.77 18. 10:19.690 --> 10:20.090 Yeah. 10:20.130 --> 10:29.410 So 2.7 18 which governs the natural exponential decay and example calculations, is at zero t. 10:29.450 --> 10:38.010 Here in the order zero nanoseconds we have zero at the. 10:38.290 --> 10:42.290 If t equals one nanoseconds, which is one time constant. 10:42.450 --> 10:44.570 Basically it will. 10:44.570 --> 10:57.370 We will get 3.1 if we use this formula and add six nanoseconds six time constants. 10:58.130 --> 11:05.810 What we will have is we will basically reach our final voltage, which is five volts approximately. 11:06.330 --> 11:12.210 Now by this time the current is steady and the inductor is no longer resisting the current flow. 11:13.330 --> 11:18.290 And in real circuits, inductors serve as guardians. 11:18.330 --> 11:21.250 They suppress certain surges. 11:21.370 --> 11:24.970 They prevent voltage spikes from damaging sensitive components. 11:25.810 --> 11:31.570 They ensure steady, clean current delivery to CPUs and high frequency circuits. 11:31.930 --> 11:39.930 And without inductors, modern electronics would be far more vulnerable to instability and failure and 11:39.930 --> 11:46.570 even tiny changes measured in nanoseconds can decide whether a system works smoothly or crashes. 11:47.330 --> 11:57.010 So summary points of this lecture is inductors stored magnetic energy and resists changes in current. 11:57.730 --> 12:07.450 The equation v t describes the direct relationship between current changes and inductor voltage. 12:08.250 --> 12:16.170 The time constant t error here measures how fast an inductor reacts. 12:17.010 --> 12:18.490 Exponential curves. 12:18.490 --> 12:25.810 Here describes the natural way voltages rise and fall in these circuits. 12:26.570 --> 12:35.650 So inductors are essentially a protecting, smoothing, and stabilizing modern electronic components. 12:35.690 --> 12:37.610 Now thank you for watching this lecture. 12:37.650 --> 12:40.410 My name is typhoon and I'm waiting you in the next lecture.