Today, let's dive into one of the most important building blocks of electronics, which is capacitors.
We encounter capacitors everywhere from computers to smartphones, and understanding them deeply will
help you become much more confident when designing and analyzing circuits.
So what exactly is a capacitor?
A capacitor is a component that stores energy in the form of an electric field created by accumulated
electric charge on two conductive plates, separated by an insulating material.
In simpler words, think of a capacitor like a small energy tank.
It fills up the electric charge and can be released when it's needed.
Now, when you first connect the capacitor into a circuit, something interesting happens.
Current initially flows into it very easily, current very easily, and almost like it's just a piece
of wire.
But here's the key.
Now, instead of letting that current pass straight through, the capacitor gradually builds up electrical
charge on its plates.
As the charge builds, electrical field forms between the plates and this electric field starts resisting
more current flowing in.
That's why the current naturally decreases over time.
Now, in short, at the beginning it is easy.
Over time it is harder and harder to current to flow.
And when the capacitor is fully charged, current almost stops.
Now, since it takes time for this electrical field to build up, capacitors are extremely useful when
we want to smooth out sudden changes in voltage.
Now, for example, if there's a sudden surge in a current.
The capacitor absorbs some of that surge, and if the current suddenly drops, the capacitor releases
its stored charge to keep the voltage steady.
Now, this property is crucial in digital circuits, where the sudden voltage spikes could otherwise
cause errors and burn components.
Now let's get a bit mathematical here.
I don't like that.
But don't worry, I will walk you through slowly.
So the voltage across the capacitor changes with time.
Now we can describe this equation with this v time.
Now let's break it down very carefully.
Now v here means the voltage across the capacitor at the specific time.
Now this is what time this I t here is the current Flowing into the capacitor at any moment.
And the see here is the capacitance value measured in farads.
And this symbol, called integral, simply means adding up very tiny contributions of current over time.
Now, if you're not familiar with the calculus, imagine filling a bucket with tiny drops of water.
Here, every small amount of current flowing in adds a drop of voltage to the capacitor over time.
If those drops add up, the voltage builds up.
Now, the important idea here is the more current that flows into the capacitor, the more voltage it
develops.
But it happens gradually.
Gradually.
Not like instantly.
Here.
Like this.
It happens gradually.
And now let's look at a real example to make all this more concrete.
This simple circuit has five volts of power supply, a switch, a one kilo ohm resistor and one farad
capacitor.
Now, when the switch is first closed, here's a story that unfolds here.
At the very beginning we have t which equals to zero.
Now the capacitor here is completely empty.
It behaves like a var.
Now the full five volts appears across the resistor.
If the circuit is closed, let's close the circuit and see what will happen.
The full 5.0V appears Here's across the resistor.
The voltage across the capacitor, which is what v b c is zero volts.
The current is maximum.
And the initial current calculation you will learn here is I.
Here is initial 5.0V.
One kilo ohms equals what 5.0mA.
Now this is simple.
Ohm's law here which you learned in previous lecture which is current equals voltage divided by resistance.
And as the time passes, the capacitor starts building up charge voltage across the capacitor V BC starts
rising as the time goes on and the voltage across the resistor start dropping, which is what v a p
v a b is not stopping voltage, a to B starts dropping and the current is gradually decreases.
The energy flow follows this important rule here.
5.0V initial time multiplied by r v and b c here b c and time.
Now this, uh, formula here just says the battery voltage must always be shared between the resistor
and the capacitor.
And eventually, if we had enough time to come into the steady state, the capacitor voltage reaches
5.0V and the resistor voltage, which is five volts, and the resistor voltage drops to zero and almost
no current falls to nearly zero.
Not to zero, but nearly zero.
Maybe 0.01 and zero point.
Because we have extra component here and takes it takes energy and capacitor.
Capacitors are not 100% efficient here and that's why we have this current.
Now at first the circuit behaves like it's just a resistor here.
Over time, the capacitor charges up stealing voltage from the resistor.
And until it finally blocks and the current flows completely without any problem.
And now what you're seeing here is this is basically a voltage and the time graph of this capacitor
on our circuit here.
Now let's take a closer look and a deeper look on this figure.
Now this graph is more than just lines.
Now it just tells the full story of how capacitor behaves on the left y axis, which shows the voltage
across the capacitor v b c v b c on the right y axis shows the voltage across the resistor v a c no
v a b here.
Now the scales are opposite.
As one voltage rises, the other falls.
Now the current is at its maximum value.
So how we basically draw that we will use a different color.
So what.
It will go up to the one volt.
And over there just stay there or maybe write it more curved.
Yeah.
No it will.
On the fourth millisecond.
And yes, that's basically how our voltage graph behaves.
So at t0 t is a time.
By the way t0 v BC is zero volts because the capacitor has no charge here.
We have just started our circuit.
Right.
Let's also let's also close our switch.
And yeah in the VAB the a b is five volts because the full supply voltage is across.
The resistor current is at its maximum value.
The voltage VB across the capacitor increases exponentially.
The voltage V a b across the resistor.
Decrease exponentially.
So this is basically how it is.
Also we will use this color.
As I said this is what this is a opposite scale graph.
This is another graph which is VBC and VAB.
So y exponential you may ask here in the beginning the capacitor charges quickly because there is a
large voltage difference pushing the current.
So 5.0V is a lot bigger than 0.0V or 0.0. 5V or 3V.
Right.
But 5.0V is not bigger than 4.8V, for example.
Right?
So in the beginning, the capacitor charges quickly because there is a large voltage difference pushing
the current up.
As the capacitor fills up, the voltage difference gets smaller and smaller and the and the charging
slows down, but not stops.
Remember, capacitors are not 100% efficient.
This slowing down is characteristics of exponential behavior and the voltage across the capacitor at
any time t is v bc time v eight multiplied by one minus minus t r c where v eight.
Here is a supply voltage of 5.0V.
In this case, the e here is the base of the natural logarithm approximately 4.71 and r c.
Here is the time constant.
So at one time constant, which is one time constant, is basically one millisecond.
So it is after the one millisecond, the capacitor has charged up to 63% of its final voltage.
And at six time constant six time constants, we have what we have approximately five volts.
And and how we get this five volts.
So in this case t is 6.0 milliseconds and v eight is basically five volts E t is basically again same
6.0 milliseconds.
And yeah use we will get approximately 5.0V Probably less than 5.0V.
Meanwhile, the voltage across the resistor A B drops in the opposite manner.
It starts with 5.0V.
So remember capacitor starts with.
It starts with 0.0V.
But resistor starts from 5.0V.
Because the power source is 5.0V it's giving 5.0V to resistor.
And yeah it starts with 5.0V and it falls exponentially to zero volts, almost zero volts as the capacitor
charges up.
And the key insight for you is the capacitor and resistor trade voltage like they are giving each other
voltage.
This is resistor this capacitor and.
Yeah.
And the faster the trade which is faster trade means smaller RC the faster the circuit responds, and
after about five six time constants, the circuit reaches a steady state and summary.
Key points for you is capacitors charge gradually and resist instant changes.
Current starts high and falls to near zero as the capacitor fills up and the time constant r c predicts
how quickly the capacitor changes.
And this is the formula.
And after the after about.
In this case, after about five six milliseconds or five six time constants, the capacitor is almost
fully charged and the capacitor stores energy as an electric field, not as a continuous current.
Now that's it for our lecture.
Thank you for watching and I'm waiting you in the next lecture.