All right.
Now that we have covered capacitors and how they store energy in an electric field, it is time to explore
their magnetic cousin, which is inductors.
What is an inductor, you may ask?
An inductor is a fundamental passive electronic component that stores energy in a magnetic field.
This magnetic field forms whenever a current flows through the coil of wire inside the inductor.
To give you a deeper analogy, if capacitors resist sudden changes in voltage, inductors resist sudden
changes in current.
So imagine trying to install a spin up a heavy flywheel.
It resists your effort initially, but once it gets going, it keeps spinning easily.
Now that's exactly how an inductor behaves toward electric current.
How does an inductor behave?
So when a voltage is applied to a circuit containing an inductor, initially the, the inductor strongly
resists any change in current.
It behaves almost like an open circuit.
As time passes, the inductor builds up a magnetic field, gradually allowing more current to flow,
and eventually, once the magnetic field is fully established, the inductor acts like a simple piece
of wire, which is low resistance.
So simple summary.
At first, inductor blocks certain current.
Later inductor allows current to pass, and finally inductor behaves like a short wire or DC in a steady
state.
Now this unique behavior is essential in controlling and smoothing electrical signals, especially in
fast switching circuits.
So real world example of inductors is we can say that inductors are used in computers.
So if you open your computer motherboard and now near the CPU, you will see a notice donut shaped components
wrapped in a copper wire.
Now these are inductors that we are talking here.
Now their role is to filter and smooth the voltage feeding to the CPU.
Now, without them, tiny fluctuations in power could cause data corruption, crashes, or even hardware
damage.
Inductors are critical because they stabilize the current, preventing sudden spikes that could disrupt
sensitive microprocessors.
So how inductors react mathematically.
You may ask?
So we have formula which is basically the mathematical relationship describing an inductor is.
Now let's break it down carefully here.
So here As always, you will learn from the previous lectures.
VTI is the instantaneous voltage across the inductor.
T here is time.
Remember L here is the inductance.
Inductance measured in Henries or H, indicating how strongly the inductor resists changes in current.
And d I t divided by d t.
Here is the derivative of current with respect to time, describing how fast the current is trying to
change.
If we interpret this basically a fast changing current which means large, this results in a large opposing
voltage across the inductor.
A slow or no change in current results in little to no voltage across the inductor.
In everyday language, you can say that the faster you try to change the current, the harder the inductor
fights back by generating a voltage.
Now this behavior protects circuits against damaging current surges, as we always do.
We have explained this with a simple circuit.
Now in this circuit we have a power supply five volts.
Also, we have an inductor.
This inductor is actually not kilohertz.
This is how you describe an inductor.
And we have a resistor which is one kilo ohms again.
So when you close the switch here initially the inductor takes the full five voltage which basically
acts like an open circuit.
So no current flows through the resistor here right now.
And as time goes on.
Like you see here, the magnetic field builds up in this inductor.
So the inductor voltage decreases, resistor voltage increases.
And finally the resistor voltage gets five volts here.
In this case you can see it's a BC.
So B to C gets highest voltage over time.
And you can see inductor resistance almost comes closer to non-zero but not fully zero here.
So basically finally the resistor gets full five volts and steady current flows.
And if we go to time constant we have the time here.
So the time constant T tells us how quickly the current increases.
And in our case if we try to calculate that At 1.01 ten.
Sixth power 1.0 multiplied by ten three power ohm.
You see, this is basically three because it is 1000Ω, right?
And yeah, basically 1.0 ten power negative nine is 1.0 nanoseconds.
We get here.
So after about one nanoseconds the current has reached 63% of its final value here.
Oops.
Yeah.
Here.
Almost estimated here.
So here it is 60%.
And after about five six nanoseconds.
It, as you can see here, almost, but not it's not ever 100% because not in electronics, there's
no component that is almost 100% efficient.
But we can say that it is almost 100% the current reached here.
And as we calculate it here, it just needs five six nanoseconds to reach almost 100%.
And after that it will go on stable.
So basically we can use the inductors as stabilizers for the current.
And in ultrafast circuits like CPUs, even nanoseconds.
Here matters greatly considering how fast the CPUs are today.
And here you can see we have a graph of our circuits, inductors, how it behaves, how it acts.
So this graph shows the how the voltage or how the voltages behave over time.
After closing the switch in upper circuit here in the left y axis we can see it shows the voltage of
BC.
So this basically means the voltage across the resistor voltage B and C, and in the right y axis it
shows the voltage AB which is a b here.
So it includes in voltage AB it includes inductor and voltage BC.
It includes the resistor here.
And x axis is basically time which is in nanoseconds.
So at time zero we have zero volts which across BC because no current yet.
So no voltage across the resistors and in the VAB.
And if the time is zero, you can see that it is the entire power supply voltage across inductor.
As the time increases, BC rises exponentially toward five volts.
And the a b here falls toward zero volts.
Here, because the change is fast at first, then it slows down as the circuit reaches equilibrium.
So you may ask why exponential?
Because a change is fast at first, then slows down as the circuit reaches top goal here and we have
the voltage formula V, a, b is basically T 5.0V multiplied by one e times t.
So where this e here is basically Euler's number approximately 2.77 18.
Yeah.
So 2.7 18 which governs the natural exponential decay and example calculations, is at zero t.
Here in the order zero nanoseconds we have zero at the.
If t equals one nanoseconds, which is one time constant.
Basically it will.
We will get 3.1 if we use this formula and add six nanoseconds six time constants.
What we will have is we will basically reach our final voltage, which is five volts approximately.
Now by this time the current is steady and the inductor is no longer resisting the current flow.
And in real circuits, inductors serve as guardians.
They suppress certain surges.
They prevent voltage spikes from damaging sensitive components.
They ensure steady, clean current delivery to CPUs and high frequency circuits.
And without inductors, modern electronics would be far more vulnerable to instability and failure and
even tiny changes measured in nanoseconds can decide whether a system works smoothly or crashes.
So summary points of this lecture is inductors stored magnetic energy and resists changes in current.
The equation v t describes the direct relationship between current changes and inductor voltage.
The time constant t error here measures how fast an inductor reacts.
Exponential curves.
Here describes the natural way voltages rise and fall in these circuits.
So inductors are essentially a protecting, smoothing, and stabilizing modern electronic components.
Now thank you for watching this lecture.
My name is typhoon and I'm waiting you in the next lecture.