[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.17,0:00:04.04,Default,,0000,0000,0000,,>> Okay. Now let's talk about what happens to voltage and current,
Dialogue: 0,0:00:04.04,0:00:07.79,Default,,0000,0000,0000,,and we first turn on a voltage source let's say we first took up the battery,
Dialogue: 0,0:00:07.79,0:00:11.76,Default,,0000,0000,0000,,it's going to start putting charges on top of this plate,
Dialogue: 0,0:00:11.76,0:00:15.62,Default,,0000,0000,0000,,which is then going to force charges away from this plate and again this flow of current.
Dialogue: 0,0:00:15.62,0:00:17.82,Default,,0000,0000,0000,,Current starts to flow immediately.
Dialogue: 0,0:00:17.82,0:00:23.37,Default,,0000,0000,0000,,Its largest at the start and gradually as the charges fill up on his plate,
Dialogue: 0,0:00:23.37,0:00:25.83,Default,,0000,0000,0000,,there'll be no current at the end when the plates are all full.
Dialogue: 0,0:00:25.83,0:00:28.47,Default,,0000,0000,0000,,So, current begins to start immediately
Dialogue: 0,0:00:28.47,0:00:31.72,Default,,0000,0000,0000,,and is largest at the beginning and then falls down to zero.
Dialogue: 0,0:00:31.72,0:00:37.25,Default,,0000,0000,0000,,Meanwhile, the current starts
Dialogue: 0,0:00:37.25,0:00:40.34,Default,,0000,0000,0000,,immediately but then when the plates are full it goes to zero.
Dialogue: 0,0:00:40.34,0:00:42.54,Default,,0000,0000,0000,,So, what does that look like the current?
Dialogue: 0,0:00:42.54,0:00:46.43,Default,,0000,0000,0000,,Here is a picture of an interesting circuit where we have a switch that's going to
Dialogue: 0,0:00:46.43,0:00:50.51,Default,,0000,0000,0000,,take this 10-volt battery and turn it on to start charging this capacitor.
Dialogue: 0,0:00:50.51,0:00:53.82,Default,,0000,0000,0000,,We know that the current is dq dt that that's also
Dialogue: 0,0:00:53.82,0:00:57.35,Default,,0000,0000,0000,,equal to the capacitance times the change in voltage with respect to time.
Dialogue: 0,0:00:57.35,0:01:00.54,Default,,0000,0000,0000,,So, as I turned this on, let's see what's going to happen.
Dialogue: 0,0:01:00.54,0:01:02.09,Default,,0000,0000,0000,,When I first turn it on,
Dialogue: 0,0:01:02.09,0:01:04.64,Default,,0000,0000,0000,,it's going to go up to its peak current and then it's
Dialogue: 0,0:01:04.64,0:01:08.37,Default,,0000,0000,0000,,going to gradually go down to zero as the plates get full.
Dialogue: 0,0:01:08.50,0:01:13.19,Default,,0000,0000,0000,,In fact, it's peak current is going to occur up
Dialogue: 0,0:01:13.19,0:01:17.14,Default,,0000,0000,0000,,here when the capacitor is effectively a short circuit.
Dialogue: 0,0:01:17.14,0:01:19.30,Default,,0000,0000,0000,,So, look right here when we first started,
Dialogue: 0,0:01:19.30,0:01:22.02,Default,,0000,0000,0000,,all the current can go into that faster.
Dialogue: 0,0:01:22.02,0:01:24.31,Default,,0000,0000,0000,,At the very beginning when we had a big change,
Dialogue: 0,0:01:24.31,0:01:26.90,Default,,0000,0000,0000,,this capacitor acts like a short circuit.
Dialogue: 0,0:01:26.90,0:01:29.13,Default,,0000,0000,0000,,So, what will the current be?
Dialogue: 0,0:01:29.13,0:01:32.04,Default,,0000,0000,0000,,It will be this voltage divided by that resistance,
Dialogue: 0,0:01:32.04,0:01:35.10,Default,,0000,0000,0000,,and in fact, right there, that's what it is.
Dialogue: 0,0:01:35.10,0:01:37.65,Default,,0000,0000,0000,,Is simply what everything at time t equal to zero,
Dialogue: 0,0:01:37.65,0:01:39.73,Default,,0000,0000,0000,,and then we have this exponential decay.
Dialogue: 0,0:01:39.73,0:01:43.03,Default,,0000,0000,0000,,The speed of the decay depends on something that we call the time constant,
Dialogue: 0,0:01:43.03,0:01:47.70,Default,,0000,0000,0000,,tau that is equal to R times C for a series resistor capacitor circuit.
Dialogue: 0,0:01:47.70,0:01:49.23,Default,,0000,0000,0000,,If I have for example,
Dialogue: 0,0:01:49.23,0:01:50.46,Default,,0000,0000,0000,,R is one kilo ohm,
Dialogue: 0,0:01:50.46,0:01:52.49,Default,,0000,0000,0000,,C is one microfarad and this voltage,
Dialogue: 0,0:01:52.49,0:01:54.82,Default,,0000,0000,0000,,this is exactly what my currents would look like,
Dialogue: 0,0:01:54.82,0:01:58.96,Default,,0000,0000,0000,,starting out at VS over R and ending at zero.
Dialogue: 0,0:01:58.96,0:02:02.69,Default,,0000,0000,0000,,The time constant tells us that as this exponential decreases,
Dialogue: 0,0:02:02.69,0:02:05.48,Default,,0000,0000,0000,,it will reach 36 percent of its original value,
Dialogue: 0,0:02:05.48,0:02:08.86,Default,,0000,0000,0000,,at the time constant tau equals RC.
Dialogue: 0,0:02:08.86,0:02:12.15,Default,,0000,0000,0000,,Okay. Now what happens when we first turn on the voltage.
Dialogue: 0,0:02:12.15,0:02:14.72,Default,,0000,0000,0000,,Well, originally there are no charges on the top plate,
Dialogue: 0,0:02:14.72,0:02:16.48,Default,,0000,0000,0000,,there are no charges on the bottom plate,
Dialogue: 0,0:02:16.48,0:02:20.70,Default,,0000,0000,0000,,and so the total voltage across here would start out as zero.
Dialogue: 0,0:02:20.70,0:02:23.66,Default,,0000,0000,0000,,But as we gradually add up all of these charges,
Dialogue: 0,0:02:23.66,0:02:25.88,Default,,0000,0000,0000,,then there's going to be a large voltage at the end.
Dialogue: 0,0:02:25.88,0:02:31.43,Default,,0000,0000,0000,,So, the voltage is the integral of the current over time with the capacitance inverted.
Dialogue: 0,0:02:31.43,0:02:34.08,Default,,0000,0000,0000,,So, right here's my case.
Dialogue: 0,0:02:34.08,0:02:37.12,Default,,0000,0000,0000,,I'm going to be integrating the current over time.
Dialogue: 0,0:02:37.12,0:02:38.50,Default,,0000,0000,0000,,This is what it looks like.
Dialogue: 0,0:02:38.50,0:02:42.11,Default,,0000,0000,0000,,My voltage starts out at zero and it ends up that Vs.
Dialogue: 0,0:02:42.11,0:02:45.58,Default,,0000,0000,0000,,The voltage is one over the capacitance times the integral of time,
Dialogue: 0,0:02:45.58,0:02:50.68,Default,,0000,0000,0000,,and if you look at that, that's going to be Vs times 1 minus e to the minus t over tau.
Dialogue: 0,0:02:50.68,0:02:52.68,Default,,0000,0000,0000,,Again, it's the same time constant.
Dialogue: 0,0:02:52.68,0:02:59.12,Default,,0000,0000,0000,,So, the voltage reaches 66 percent of its value at the time constant RC.
Dialogue: 0,0:02:59.12,0:03:03.36,Default,,0000,0000,0000,,So, here's the answer to what does a capacitor do to a voltage and current?
Dialogue: 0,0:03:03.36,0:03:06.22,Default,,0000,0000,0000,,With the current plot we looked at and here's the voltage plot.
Dialogue: 0,0:03:06.22,0:03:08.12,Default,,0000,0000,0000,,Steady state would be long time,
Dialogue: 0,0:03:08.12,0:03:10.76,Default,,0000,0000,0000,,like after the switch has been closed for a long time,
Dialogue: 0,0:03:10.76,0:03:14.96,Default,,0000,0000,0000,,and that would say there would be no current and that there would be a large voltage.
Dialogue: 0,0:03:14.96,0:03:17.84,Default,,0000,0000,0000,,At time t equal to zero when there is a very big change,
Dialogue: 0,0:03:17.84,0:03:19.67,Default,,0000,0000,0000,,the capacitor acts as a short circuit.
Dialogue: 0,0:03:19.67,0:03:22.34,Default,,0000,0000,0000,,The time t equal to infinity when it's all charged up,
Dialogue: 0,0:03:22.34,0:03:24.59,Default,,0000,0000,0000,,it acts like an open circuit.
Dialogue: 0,0:03:24.59,0:03:27.16,Default,,0000,0000,0000,,Now what are the implications of that?
Dialogue: 0,0:03:27.16,0:03:30.14,Default,,0000,0000,0000,,When we have something that we want to charge and discharge,
Dialogue: 0,0:03:30.14,0:03:33.81,Default,,0000,0000,0000,,instead of being able to do a square wave like they might have liked,
Dialogue: 0,0:03:33.81,0:03:36.14,Default,,0000,0000,0000,,we always end up with some stray capacitance and make
Dialogue: 0,0:03:36.14,0:03:40.12,Default,,0000,0000,0000,,our square wave looks like this charging, discharging plot.
Dialogue: 0,0:03:40.12,0:03:42.26,Default,,0000,0000,0000,,How do we use capacitors?
Dialogue: 0,0:03:42.26,0:03:45.08,Default,,0000,0000,0000,,Here are two examples where we use them for energy storage.
Dialogue: 0,0:03:45.08,0:03:48.62,Default,,0000,0000,0000,,This disposable camera for example has two batteries and a capacitor
Dialogue: 0,0:03:48.62,0:03:52.31,Default,,0000,0000,0000,,inside in order to make the flash that you use when you take a picture.
Dialogue: 0,0:03:52.31,0:03:55.28,Default,,0000,0000,0000,,The capacitance between the clouds and the earth
Dialogue: 0,0:03:55.28,0:03:58.68,Default,,0000,0000,0000,,is what creates the ability for lightning to strike.
Dialogue: 0,0:03:58.68,0:04:03.60,Default,,0000,0000,0000,,We can also use capacitors to stabilize power for example to the reduce ripple.
Dialogue: 0,0:04:03.60,0:04:06.74,Default,,0000,0000,0000,,Here's a case where we've put in a power supply and let's suppose that
Dialogue: 0,0:04:06.74,0:04:10.06,Default,,0000,0000,0000,,sometimes it was a little more than nine volts and sometimes it was a little less,
Dialogue: 0,0:04:10.06,0:04:13.31,Default,,0000,0000,0000,,but that our circuit over here wants exactly nine volts.
Dialogue: 0,0:04:13.31,0:04:16.79,Default,,0000,0000,0000,,In that case, this capacitor can take a little bit of that
Dialogue: 0,0:04:16.79,0:04:20.98,Default,,0000,0000,0000,,away when it's too high and return a little bit back, when it is low.
Dialogue: 0,0:04:20.98,0:04:25.56,Default,,0000,0000,0000,,The capacitor effectively storing the excess and release it when it is needed.
Dialogue: 0,0:04:25.56,0:04:29.02,Default,,0000,0000,0000,,Now let's talk about low pass and high pass filters.
Dialogue: 0,0:04:29.02,0:04:31.14,Default,,0000,0000,0000,,A low pass signal is going to allow
Dialogue: 0,0:04:31.14,0:04:34.78,Default,,0000,0000,0000,,a constant value to go through but not the high frequency noise.
Dialogue: 0,0:04:34.78,0:04:37.04,Default,,0000,0000,0000,,So, here's a series RC circuit,
Dialogue: 0,0:04:37.04,0:04:40.25,Default,,0000,0000,0000,,where remember that if I have a change,
Dialogue: 0,0:04:40.25,0:04:44.58,Default,,0000,0000,0000,,a fast changing thing that this thing acts like an open circuit.
Dialogue: 0,0:04:44.58,0:04:49.54,Default,,0000,0000,0000,,So, it allows the low frequency to go through but not the high frequency.
Dialogue: 0,0:04:49.54,0:04:50.96,Default,,0000,0000,0000,,Here's another example.
Dialogue: 0,0:04:50.96,0:04:53.06,Default,,0000,0000,0000,,What does this look like without the capacitor?
Dialogue: 0,0:04:53.06,0:04:55.10,Default,,0000,0000,0000,,Looks like an inverting amplifier.
Dialogue: 0,0:04:55.10,0:04:58.28,Default,,0000,0000,0000,,Now let's suppose that we tried to send a DC value through.
Dialogue: 0,0:04:58.28,0:04:59.72,Default,,0000,0000,0000,,Well, the DC value,
Dialogue: 0,0:04:59.72,0:05:01.94,Default,,0000,0000,0000,,this capacitor still acts like an open circuit.
Dialogue: 0,0:05:01.94,0:05:05.39,Default,,0000,0000,0000,,So, it just acts like an inverting amplifier that you've always seen before.
Dialogue: 0,0:05:05.39,0:05:07.45,Default,,0000,0000,0000,,The low pass signal goes through,
Dialogue: 0,0:05:07.45,0:05:11.58,Default,,0000,0000,0000,,but now what if I wanted to send a grasp changing a high frequency signal.
Dialogue: 0,0:05:11.58,0:05:14.32,Default,,0000,0000,0000,,In that case, the capacitor would act like a short circuit.
Dialogue: 0,0:05:14.32,0:05:16.14,Default,,0000,0000,0000,,I'll be shorting out my R2.
Dialogue: 0,0:05:16.14,0:05:23.86,Default,,0000,0000,0000,,Remember what the amplification for inverting amplifiers,
Dialogue: 0,0:05:23.86,0:05:30.46,Default,,0000,0000,0000,,remember that the gain is equal to minus RF divided by RS,
Dialogue: 0,0:05:30.46,0:05:34.13,Default,,0000,0000,0000,,and then in this case the RF is R2,
Dialogue: 0,0:05:34.13,0:05:36.64,Default,,0000,0000,0000,,but if I made RF equal to zero,
Dialogue: 0,0:05:36.64,0:05:38.13,Default,,0000,0000,0000,,then my game would be zero.
Dialogue: 0,0:05:38.13,0:05:40.94,Default,,0000,0000,0000,,So, the high frequency signal that will come out with the zero.
Dialogue: 0,0:05:40.94,0:05:44.61,Default,,0000,0000,0000,,The capacitor allows the low frequency to go through this circuit,
Dialogue: 0,0:05:44.61,0:05:49.98,Default,,0000,0000,0000,,goes through R2 that takes the high frequency through here and basically equals to zero.
Dialogue: 0,0:05:49.98,0:05:53.12,Default,,0000,0000,0000,,This allows the capacitor to work as an integrator.
Dialogue: 0,0:05:53.12,0:05:55.58,Default,,0000,0000,0000,,Notice here's the RC circuit right here.
Dialogue: 0,0:05:55.58,0:05:59.18,Default,,0000,0000,0000,,It's taking this square wave and it's producing this output.
Dialogue: 0,0:05:59.18,0:06:00.100,Default,,0000,0000,0000,,Remember what integration does?
Dialogue: 0,0:06:00.100,0:06:02.98,Default,,0000,0000,0000,,It finds the area under the curve.
Dialogue: 0,0:06:02.98,0:06:06.20,Default,,0000,0000,0000,,When I first made my step up the area is zero,
Dialogue: 0,0:06:06.20,0:06:08.63,Default,,0000,0000,0000,,and gradually as I'm adding up, adding up,
Dialogue: 0,0:06:08.63,0:06:10.25,Default,,0000,0000,0000,,adding up the area of the curve,
Dialogue: 0,0:06:10.25,0:06:12.32,Default,,0000,0000,0000,,it builds up the maximum voltage.
Dialogue: 0,0:06:12.32,0:06:14.09,Default,,0000,0000,0000,,When I take a negative value,
Dialogue: 0,0:06:14.09,0:06:15.86,Default,,0000,0000,0000,,it starts subtracting off that value.
Dialogue: 0,0:06:15.86,0:06:17.99,Default,,0000,0000,0000,,So, there's no charging discharging though.
Dialogue: 0,0:06:17.99,0:06:23.14,Default,,0000,0000,0000,,I can literally use this capacitor circuit to integrate signals that are coming in.
Dialogue: 0,0:06:23.14,0:06:26.78,Default,,0000,0000,0000,,Here's a high pass filter design or DC block.
Dialogue: 0,0:06:26.78,0:06:31.84,Default,,0000,0000,0000,,In this case, notice I've just switched the location of my capacitor and my resistor.
Dialogue: 0,0:06:31.84,0:06:34.68,Default,,0000,0000,0000,,If I were sending a DC signal through,
Dialogue: 0,0:06:34.68,0:06:38.50,Default,,0000,0000,0000,,this capacitor it would look like an open circuit and my output voltage would be zero.
Dialogue: 0,0:06:38.50,0:06:41.96,Default,,0000,0000,0000,,Nothing will come out, but if I had a high frequency signal from
Dialogue: 0,0:06:41.96,0:06:46.48,Default,,0000,0000,0000,,this capacitor would act like a short circuit and the full voltage would come out.
Dialogue: 0,0:06:46.48,0:06:49.24,Default,,0000,0000,0000,,Now here's my inverting amplifier again.
Dialogue: 0,0:06:49.24,0:06:53.78,Default,,0000,0000,0000,,Remember, that the gain is equal to minus RF which is R2 in
Dialogue: 0,0:06:53.78,0:06:58.72,Default,,0000,0000,0000,,this case divided by RS which is R1.
Dialogue: 0,0:06:58.72,0:07:02.34,Default,,0000,0000,0000,,Well, if I have a DC signal my RS is infinity,
Dialogue: 0,0:07:02.34,0:07:04.65,Default,,0000,0000,0000,,and so my full voltage comes out.
Dialogue: 0,0:07:04.65,0:07:09.04,Default,,0000,0000,0000,,If I have an AC or very high frequency signal, I have a short circuit,
Dialogue: 0,0:07:09.04,0:07:13.68,Default,,0000,0000,0000,,and that means that I get no frequency, no signal out.
Dialogue: 0,0:07:13.68,0:07:18.95,Default,,0000,0000,0000,,So, high pass signals come through but low pass signals do not.
Dialogue: 0,0:07:18.95,0:07:21.40,Default,,0000,0000,0000,,That allows me to do differentiation.
Dialogue: 0,0:07:21.40,0:07:24.26,Default,,0000,0000,0000,,That means that I want to emphasize the changes.
Dialogue: 0,0:07:24.26,0:07:25.76,Default,,0000,0000,0000,,Here's an up and here's a down.
Dialogue: 0,0:07:25.76,0:07:27.18,Default,,0000,0000,0000,,If I did the derivative,
Dialogue: 0,0:07:27.18,0:07:32.21,Default,,0000,0000,0000,,I would see this and I will see that for this is what my capacitor does,
Dialogue: 0,0:07:32.21,0:07:37.97,Default,,0000,0000,0000,,it seems a little but there's my first step and here's my second step.
Dialogue: 0,0:07:37.97,0:07:41.70,Default,,0000,0000,0000,,This is the differentiation of the square length.
Dialogue: 0,0:07:41.92,0:07:45.20,Default,,0000,0000,0000,,So, basically we have covered these four topics.
Dialogue: 0,0:07:45.20,0:07:46.52,Default,,0000,0000,0000,,What is capacitance?
Dialogue: 0,0:07:46.52,0:07:48.48,Default,,0000,0000,0000,,How does it relate to current and charges?
Dialogue: 0,0:07:48.48,0:07:50.09,Default,,0000,0000,0000,,How do the various parameters of
Dialogue: 0,0:07:50.09,0:07:53.69,Default,,0000,0000,0000,,the capacitor matter and what does it do to a voltage and a current?
Dialogue: 0,0:07:53.69,0:07:56.88,Default,,0000,0000,0000,,Thank you very much for your attention.