In this lecture, we're going to start working on AC circuit analysis.

And so the first thing we have to do is talk about two new circuit components,

capacitors and inductors. And then, after introducing those, we're

going to talk about decomposing signals into their sinusoidal components and the

idea of phasors. Then with all of those tools, we can

start to do some AC circuit analysis, and then using those techniques, we're going

to look at a few simple filters. Low pass and high pass filters built out

of resistors, capacitors, and inductors. We'll start by talking about capacitors

first. So, capacitors are nothing more than a

pair of metal plates that are separated by either a vacuum or maybe some kind of

a dielectric material. And there's say a gap, d, in the plates,

and on those plates, we can place some charge.

So we can put plus charge on one plate and minus charge on the other plate, and

you know that if I segregate charge in that way, I get an electric field

pointing from the plus to the minus charge, and so there's a, there's an

electric field contained inside the capacitor.

Now, the electric field in the capacitor gives rise to a voltage difference

between the terminals. So this is a device that when I put

charge on the two plates, there's a voltage difference between the two

terminals. Now, energy is stored in a capacitor in

the form of the electric field contained in the dielectric material, and you

remember from before that the electric field is the voltage divided by the

distance from the the plus charged to the minus charged plates.

Or we can rewrite that as the voltage is the electric field times that distance,

or the gap in the capacitor. Now the capacitance of this structure Is

the ability of this device to store a charge, or the capacity of the device to

store a charge. Now, we define capacitance as the number

of Coulombs per volts. So, it's Q over V.

And capacitance is measured in farads, and so, this device has a capacitance, c,

we'll cal it, and it's defined by this relationship, q is c times v.

So, if I have, if I take this device and let's say I put one volt of potential

difference on the two plates, then there will be some amount of charge stored in

the device that is equal to the capacitance times that voltage.

So a one-farad capacitor means that if I put one volt pepit, potential difference

here, I'll get one coulomb of stored charge.

Now a 1 Farad capacitor is a very big capacitor.

typical capacitor values go from just a few picofarads, 10 to the minus 12

farads, to maybe a few hundred millifarads, 10 to the minus 3.

And picofarad-type capacitors are, you'll see them in various forms in electronic

circuits. capacitors with leads maybe a few

millimeters or maybe 5 millimeters across.

the surface-mount capacitors are typically quite small, maybe 2 or 3

millimeters in size. And so these are on the small end.

Now, millifarad capacitors or hundreds of millifarad capacitors are the, the big

ones that if you open up a piece of equipment, you see some big capacitors in

there that are part of the power supply, typically, and so these may be several

inches high and a few inches in diameter. And this is just very large coil, of two

metal electrodes, and some a kind of dialectic material, often there's there's

a a liquid in the servicing as the dialectic material, and the, these are.