>> Okay. Now let's talk about what happens to voltage and current,
and we first turn on a voltage source let's say we first took up the battery,
it's going to start putting charges on top of this plate,
which is then going to force charges away from this plate and again this flow of current.
Current starts to flow immediately.
Its largest at the start and gradually as the charges fill up on his plate,
there'll be no current at the end when the plates are all full.
So, current begins to start immediately
and is largest at the beginning and then falls down to zero.
Meanwhile, the current starts
immediately but then when the plates are full it goes to zero.
So, what does that look like the current?
Here is a picture of an interesting circuit where we have a switch that's going to
take this 10-volt battery and turn it on to start charging this capacitor.
We know that the current is dq dt that that's also
equal to the capacitance times the change in voltage with respect to time.
So, as I turned this on, let's see what's going to happen.
When I first turn it on,
it's going to go up to its peak current and then it's
going to gradually go down to zero as the plates get full.
In fact, it's peak current is going to occur up
here when the capacitor is effectively a short circuit.
So, look right here when we first started,
all the current can go into that faster.
At the very beginning when we had a big change,
this capacitor acts like a short circuit.
So, what will the current be?
It will be this voltage divided by that resistance,
and in fact, right there, that's what it is.
Is simply what everything at time t equal to zero,
and then we have this exponential decay.
The speed of the decay depends on something that we call the time constant,
tau that is equal to R times C for a series resistor capacitor circuit.
If I have for example,
R is one kilo ohm,
C is one microfarad and this voltage,
this is exactly what my currents would look like,
starting out at VS over R and ending at zero.
The time constant tells us that as this exponential decreases,
it will reach 36 percent of its original value,
at the time constant tau equals RC.
Okay. Now what happens when we first turn on the voltage.
Well, originally there are no charges on the top plate,
there are no charges on the bottom plate,
and so the total voltage across here would start out as zero.
But as we gradually add up all of these charges,
then there's going to be a large voltage at the end.
So, the voltage is the integral of the current over time with the capacitance inverted.
So, right here's my case.
I'm going to be integrating the current over time.
This is what it looks like.
My voltage starts out at zero and it ends up that Vs.
The voltage is one over the capacitance times the integral of time,
and if you look at that, that's going to be Vs times 1 minus e to the minus t over tau.
Again, it's the same time constant.
So, the voltage reaches 66 percent of its value at the time constant RC.
So, here's the answer to what does a capacitor do to a voltage and current?
With the current plot we looked at and here's the voltage plot.
Steady state would be long time,
like after the switch has been closed for a long time,
and that would say there would be no current and that there would be a large voltage.
At time t equal to zero when there is a very big change,
the capacitor acts as a short circuit.
The time t equal to infinity when it's all charged up,
it acts like an open circuit.
Now what are the implications of that?
When we have something that we want to charge and discharge,
instead of being able to do a square wave like they might have liked,
we always end up with some stray capacitance and make
our square wave looks like this charging, discharging plot.
How do we use capacitors?
Here are two examples where we use them for energy storage.
This disposable camera for example has two batteries and a capacitor
inside in order to make the flash that you use when you take a picture.
The capacitance between the clouds and the earth
is what creates the ability for lightning to strike.
We can also use capacitors to stabilize power for example to the reduce ripple.
Here's a case where we've put in a power supply and let's suppose that
sometimes it was a little more than nine volts and sometimes it was a little less,
but that our circuit over here wants exactly nine volts.
In that case, this capacitor can take a little bit of that
away when it's too high and return a little bit back, when it is low.
The capacitor effectively storing the excess and release it when it is needed.
Now let's talk about low pass and high pass filters.
A low pass signal is going to allow
a constant value to go through but not the high frequency noise.
So, here's a series RC circuit,
where remember that if I have a change,
a fast changing thing that this thing acts like an open circuit.
So, it allows the low frequency to go through but not the high frequency.
Here's another example.
What does this look like without the capacitor?
Looks like an inverting amplifier.
Now let's suppose that we tried to send a DC value through.
Well, the DC value,
this capacitor still acts like an open circuit.
So, it just acts like an inverting amplifier that you've always seen before.
The low pass signal goes through,
but now what if I wanted to send a grasp changing a high frequency signal.
In that case, the capacitor would act like a short circuit.
I'll be shorting out my R2.
Remember what the amplification for inverting amplifiers,
remember that the gain is equal to minus RF divided by RS,
and then in this case the RF is R2,
but if I made RF equal to zero,
then my game would be zero.
So, the high frequency signal that will come out with the zero.
The capacitor allows the low frequency to go through this circuit,
goes through R2 that takes the high frequency through here and basically equals to zero.
This allows the capacitor to work as an integrator.
Notice here's the RC circuit right here.
It's taking this square wave and it's producing this output.
Remember what integration does?
It finds the area under the curve.
When I first made my step up the area is zero,
and gradually as I'm adding up, adding up,
adding up the area of the curve,
it builds up the maximum voltage.
When I take a negative value,
it starts subtracting off that value.
So, there's no charging discharging though.
I can literally use this capacitor circuit to integrate signals that are coming in.
Here's a high pass filter design or DC block.
In this case, notice I've just switched the location of my capacitor and my resistor.
If I were sending a DC signal through,
this capacitor it would look like an open circuit and my output voltage would be zero.
Nothing will come out, but if I had a high frequency signal from
this capacitor would act like a short circuit and the full voltage would come out.
Now here's my inverting amplifier again.
Remember, that the gain is equal to minus RF which is R2 in
this case divided by RS which is R1.
Well, if I have a DC signal my RS is infinity,
and so my full voltage comes out.
If I have an AC or very high frequency signal, I have a short circuit,
and that means that I get no frequency, no signal out.
So, high pass signals come through but low pass signals do not.
That allows me to do differentiation.
That means that I want to emphasize the changes.
Here's an up and here's a down.
If I did the derivative,
I would see this and I will see that for this is what my capacitor does,
it seems a little but there's my first step and here's my second step.
This is the differentiation of the square length.
So, basically we have covered these four topics.
What is capacitance?
How does it relate to current and charges?
How do the various parameters of
the capacitor matter and what does it do to a voltage and a current?
Thank you very much for your attention.