[00:00:18] So, in this example, example we call example three, we are going to find the
impedance of an inductor, okay? And the whole idea is we are talking about the complex
number, and we're going to find the impedance of the inductor is a complex number. So before I
take you through the example, since we have never talked about the inductor before, let's talk
about what is an inductor.
[00:01:13] Now inductor is another circuit element. We talked about resistors before many time.
A resistor is a circuit element. Similarly an inductor is a circuit element. When you go to circuit
course, you will be talking about this inductor. Now, I have basically put the inductor is
estimated like a coil, and I'll show you that in a minute. Now,
[00:01:24] to just let you know what inductor does, it basically store energy in its magnetic field.
Okay? It creates a field which is a magnetic field. It store energy in that. And then return the
energy to the circuit whenever is required. Okay? So basically, it stores the magnetic field,
magnetic energy in the magnetic field, and then return that energy back to the circuit whenever
required. Now, an inductor is really a coil. So basically a wire with a loop. I'm basically winding
this wire on it should be a magnetic field, I'm just basically winding this. So this is a coil, okay?
And that wire then making a coil becomes an inductor. And that's what
[00:02:36] I am showing you over here. Okay? Alright so, and when you wind it, it is on a
magnetic material. Okay.
[00:02:49] So, what are the, where is the inductor used? So, inductor is used in various
communication application. And it is also, when is combined with a C, a capacitor, L and C, L is
the inductor, C is the capacitor. So in combination with a capacitor, you can combine them, and
then is used as discriminating, you can discriminate different signals. And a large inductor is also
used in power supplies to basically smooth out the signal, and smooth out, basically it takes the
AC, alternating current, and smooth out into a nice DC, which is like a battery. So those are the,
an application by the way. Also instead of, you will see later on, I take an example of RL and
RC. So, they can also be combined with RL or RC. RC is a low pass filter and RL is a high pass
filter.
So those are some of the applications of that.
[00:04:21] Now, one of the thing, we should talk about, an inductor, the impedance of an
inductor we talked about here, j omega L. L is the inductance. And inductance unit is Henry.
Henry is the unit. Also Henry is designated like that.
[00:04:54] But Henry is a very large unit. And instead of using Henrys
we will be using mostly, milliHenry or microHenrys. Okay, those are the most common units.
[00:05:11] So, the milliHenry like I have it over here 25 milliHenry. So, what 25 milliHenry?
milliHenry is 10 to the power minus 3. That's milli. milliHenry is equal to 10 the the power
minus 3 Henry. Similarly, microHenry. Micro symbol is like a, it's a µ. MicroHenry is 10 to the
power minus 6 Henry.
[00:05:40] So, the inductance of a inductor, unit of that is Henry, whereas, most of the time we'll
be using milliHenry or microHenry.
[00:05:57] So let's do that. ZL is j omega L ohms. Okay? So instead of doing that here, let's
separately calculate what omega L is. So omega L We know omega is 2 pi f. 2 pi time 60 or 120
pi. And L is 25 milliHenry.
[00:06:25] So, you must covert that milliHenry into Henry. Okay? So L must be in Henry.
[00:06:32] So, from milliHenry to Henry that is 10 to the power minus 3. Okay, so now, if I
multiply 120 pi, times 25,Okay? So that's Then that multiplied by 10 to the power minus 3. Let's
leave this 10 to the power minus three alone. So let's only multiply 120 pi times 25. That, if you
do that, it's going to give you 9,426 time 10 to the power minus 3. Okay, so now if I have ten to
the power minus 3, that gives you 9.426 ohms. Okay? So, knowing omega L, I can write now ZL.
Okay?
[00:07:27] So, in this case, this j is purely imaginary. So real part in this case is 0.
[00:07:33] So I'll write as 0 plus j 9.426 ohms. And that is the, writing the impedance in the
rectangular form. Okay? So, we have written the impedance in the rectangular form. All right,
now let's see if we can write this
[00:07:58] in the polar form. Okay, we can again use the formula like real part square plus
imaginary part square, and similarly using the arctangent, atan2. But again, I always go ahead
and so that we don't make a mistake, go ahead and plot that on the real and imaginary axis plane.
You will never go wrong. You'll know approximately what the answers should be.
[00:08:27] Okay, so let's go ahead and do that. So, we have real part and imaginary part. Okay?
So, this is 0 over here. Now, the real part is 0, so, we don't have a real part. So, imaginary part is
9.426 so this is the imaginary part. So that's my ZL, 9.426 ohms. And so this angle then is 90
degrees. So we already know my magnitude is 9.426 ohms, and the angle is 90 degree, so I can
write, state, ZL is equal to 9.426,angle of 90 degrees. Or you can write pi by 2. You can also
write this as 9.426,angle of pi divided by 2. See the way we put degrees over here. And we didn't
put anything over here. This is in radians, okay? That is the polar form of the complex number.
[00:09:35] Now, as I said you can also. That's quickly how would I do that if I go without
plotting this.
[00:09:43] So again, the magnitude of ZL is real part square, in this case is zero square plus
imaginary part square, 9.426 square, square root. And if I do that it basically, going to give me
9.426 ohm. And the angle of ZL,I can right angle of ZL or angle theta. Okay? What is that equal
to? Let me go ahead and that in the form of atan2, imaginary part, the real part. So which is
going to be (9.426, 0). And if I go ahead and calculate that, that angle is going to come out to be
90 degrees or pi by two. Okay? So again, I can same answer over here, so we have the polar
form of that 9.426 is the magnitude, and the angle is 90 degrees or pi by 2 radian.
[00:10:44] Okay so that's the polar form. And similarly the exponential
[00:10:47] form of that is going to be 9.426 e to the power j 90 degrees. Or I can write down
9.426 e to the power j pi by 2. That is the exponential form. Okay? So, we have
[00:11:15] gone through now. Again, in this case, I didn't
[00:11:19] have to write zero there. Always a good idea to show both, real part, happens to be 0,
0 plus j 9.426 ohm. And then we calculate the polar form
[00:11:31] and the exponential form.