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.