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>> Okay. Now let's talk about what happens to voltage and current,

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and we first turn on a voltage source let's say we first took up the battery,

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it's going to start putting charges on top of this plate,

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which is then going to force charges away from this plate and again this flow of current.

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Current starts to flow immediately.

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Its largest at the start and gradually as the charges fill up on his plate,

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there'll be no current at the end when the plates are all full.

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So, current begins to start immediately

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and is largest at the beginning and then falls down to zero.

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Meanwhile, the current starts

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immediately but then when the plates are full it goes to zero.

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So, what does that look like the current?

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Here is a picture of an interesting circuit where we have a switch that's going to

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take this 10-volt battery and turn it on to start charging this capacitor.

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We know that the current is dq dt that that's also

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equal to the capacitance times the change in voltage with respect to time.

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So, as I turned this on, let's see what's going to happen.

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When I first turn it on,

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it's going to go up to its peak current and then it's

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going to gradually go down to zero as the plates get full.

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In fact, it's peak current is going to occur up

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here when the capacitor is effectively a short circuit.

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So, look right here when we first started,

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all the current can go into that faster.

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At the very beginning when we had a big change,

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this capacitor acts like a short circuit.

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So, what will the current be?

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It will be this voltage divided by that resistance,

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and in fact, right there, that's what it is.

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Is simply what everything at time t equal to zero,

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and then we have this exponential decay.

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The speed of the decay depends on something that we call the time constant,

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tau that is equal to R times C for a series resistor capacitor circuit.

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If I have for example,

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R is one kilo ohm,

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C is one microfarad and this voltage,

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this is exactly what my currents would look like,

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starting out at VS over R and ending at zero.

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The time constant tells us that as this exponential decreases,

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it will reach 36 percent of its original value,

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at the time constant tau equals RC.

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Okay. Now what happens when we first turn on the voltage.

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Well, originally there are no charges on the top plate,

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there are no charges on the bottom plate,

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and so the total voltage across here would start out as zero.

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But as we gradually add up all of these charges,

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then there's going to be a large voltage at the end.

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So, the voltage is the integral of the current over time with the capacitance inverted.

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So, right here's my case.

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I'm going to be integrating the current over time.

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This is what it looks like.

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My voltage starts out at zero and it ends up that Vs.

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The voltage is one over the capacitance times the integral of time,

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and if you look at that, that's going to be Vs times 1 minus e to the minus t over tau.

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Again, it's the same time constant.

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So, the voltage reaches 66 percent of its value at the time constant RC.

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So, here's the answer to what does a capacitor do to a voltage and current?

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With the current plot we looked at and here's the voltage plot.

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Steady state would be long time,

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like after the switch has been closed for a long time,

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and that would say there would be no current and that there would be a large voltage.

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At time t equal to zero when there is a very big change,

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the capacitor acts as a short circuit.

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The time t equal to infinity when it's all charged up,

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it acts like an open circuit.

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Now what are the implications of that?

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When we have something that we want to charge and discharge,

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instead of being able to do a square wave like they might have liked,

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we always end up with some stray capacitance and make

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our square wave looks like this charging, discharging plot.

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How do we use capacitors?

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Here are two examples where we use them for energy storage.

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This disposable camera for example has two batteries and a capacitor

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inside in order to make the flash that you use when you take a picture.

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The capacitance between the clouds and the earth

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is what creates the ability for lightning to strike.

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We can also use capacitors to stabilize power for example to the reduce ripple.

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Here's a case where we've put in a power supply and let's suppose that

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sometimes it was a little more than nine volts and sometimes it was a little less,

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but that our circuit over here wants exactly nine volts.

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In that case, this capacitor can take a little bit of that

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away when it's too high and return a little bit back, when it is low.

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The capacitor effectively storing the excess and release it when it is needed.

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Now let's talk about low pass and high pass filters.

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A low pass signal is going to allow

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a constant value to go through but not the high frequency noise.

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So, here's a series RC circuit,

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where remember that if I have a change,

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a fast changing thing that this thing acts like an open circuit.

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So, it allows the low frequency to go through but not the high frequency.

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Here's another example.

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What does this look like without the capacitor?

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Looks like an inverting amplifier.

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Now let's suppose that we tried to send a DC value through.

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Well, the DC value,

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this capacitor still acts like an open circuit.

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So, it just acts like an inverting amplifier that you've always seen before.

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The low pass signal goes through,

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but now what if I wanted to send a grasp changing a high frequency signal.

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In that case, the capacitor would act like a short circuit.

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I'll be shorting out my R2.

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Remember what the amplification for inverting amplifiers,

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remember that the gain is equal to minus RF divided by RS,

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and then in this case the RF is R2,

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but if I made RF equal to zero,

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then my game would be zero.

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So, the high frequency signal that will come out with the zero.

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The capacitor allows the low frequency to go through this circuit,

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goes through R2 that takes the high frequency through here and basically equals to zero.

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This allows the capacitor to work as an integrator.

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Notice here's the RC circuit right here.

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It's taking this square wave and it's producing this output.

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Remember what integration does?

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It finds the area under the curve.

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When I first made my step up the area is zero,

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and gradually as I'm adding up, adding up,

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adding up the area of the curve,

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it builds up the maximum voltage.

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When I take a negative value,

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it starts subtracting off that value.

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So, there's no charging discharging though.

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I can literally use this capacitor circuit to integrate signals that are coming in.

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Here's a high pass filter design or DC block.

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In this case, notice I've just switched the location of my capacitor and my resistor.

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If I were sending a DC signal through,

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this capacitor it would look like an open circuit and my output voltage would be zero.

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Nothing will come out, but if I had a high frequency signal from

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this capacitor would act like a short circuit and the full voltage would come out.

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Now here's my inverting amplifier again.

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Remember, that the gain is equal to minus RF which is R2 in

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this case divided by RS which is R1.

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Well, if I have a DC signal my RS is infinity,

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and so my full voltage comes out.

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If I have an AC or very high frequency signal, I have a short circuit,

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and that means that I get no frequency, no signal out.

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So, high pass signals come through but low pass signals do not.

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That allows me to do differentiation.

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That means that I want to emphasize the changes.

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Here's an up and here's a down.

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If I did the derivative,

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I would see this and I will see that for this is what my capacitor does,

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it seems a little but there's my first step and here's my second step.

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This is the differentiation of the square length.

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So, basically we have covered these four topics.

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What is capacitance?

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How does it relate to current and charges?

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How do the various parameters of

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the capacitor matter and what does it do to a voltage and a current?

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Thank you very much for your attention.