- [Voiceover] We're now ready to start the study
of circuit analysis and to design circuits
and analyze circuits, one of the things we need to do
is have something to build circuits with
and that's what we're gonna talk about in this video.
The idea is we're gonna have three circuit elements.
These circuit elements are called resistor,
capacitor,
i-tor,
and inductor.
Okay, these are the three passive
or two-element components
or circuit elements that we're gonna use to design
a lot of different kinds of circuits.
First, I want to introduce a symbol for each one of these
so we can talk about it and making drawings of it
and first is gonna be the resistor.
Resistor symbol looks like this.
It's a zigzag line like that
representing current going through and being resisted
having to do some work.
Another symbol for resistor looks like this
used in other parts of the world
besides the United States and Japan.
That's what a resistor looks like
and the symbol we use is R.
Now for the capacitor,
capacitor symbol is actually a capacitor's built
from two conductors or metal objects
that are placed close together
and most capacitors sort of look like that
when they're actually built
and the symbol for capacitor is a C.
And finally for the inductor,
we'll do inductors like this.
An inductor is actually built from a coil of wire
and so when we draw an inductor symbol,
we draw a little coil of wire like that
and the symbol is L which is a little odd.
It could be called i but the symbol for i
was already taken by current
which is from the French for intensity
and we couldn't use C for current
because the C is used here
so it's a little quirk of our nomenclature.
All right.
Each of these components has an equation
that goes along with it
that relates the voltage to the current.
Now, I'm gonna go back here.
I'm gonna label the voltages and currents on here
in a very important convention for drawing circuits.
Let's do that.
When we talk about the voltage on a component,
we can label it however we want, plus-minus V,
and we draw the current going in.
I'll just label a little i there
and we'll do it on all these.
The current goes into the positive terminal.
The current goes into the positive terminal
so that's a V on the capacitor
and finally,
and the current goes in
and we're gonna be very consistent about this
and that's gonna keep us from making mistakes.
All right, so let's go back to our resistor
and we're gonna do the equation for a resistor.
What is the I-V equation for a resistor?
I-V equation means what relates current to voltage
and for a resistor, it's V
equals i times R
so the voltage across the resistor
is equal to the current through the resistor
times this constant of proportionality
that we call the resistance.
This has a very important name.
This is called Ohm's law
and you're gonna use this a lot
so that's Ohm's law right there.
This is Ohm's law.
Now for the IV relationship for the capacitor,
the capacitor has that property that the current
through the capacitor is proportional to the rate of change
of the voltage, not to the voltage but to the rate of change
of the voltage and the way we write that is current equals,
C is the proportionality constant,
and we write dv, dt
so this is the rate of change of voltage
with respect to time.
We multiply that by this property of this device
called capacitance and that gives us the current.
This doesn't have a special name
but I'm gonna refer to it as the capacitor equation
so now we have two equations.
Let's do the third equation which is for the inductor.
The inductor has the property very similar to the capacitor.
It has the property that the voltage across
is proportional to the time rate of change of the current
flowing through the inductor
so this is a similar but opposite of how a capacitor works.
The voltage is proportional to the time rate of change
of current and the way we write that
is voltage equals L,
di, dt.
The voltage is proportional.
The proportionality constant is the inductants.
The inductance of the inductor
and this is the time rate of change of voltage,
OH sorry, the time rate of change of current
flowing through the inductor
so this gives us our three equations.
Here they are.
These are three element equations
and we're gonna use these all the time,
right there, those three equations.
One final point I wanna make
is for both these equations of components,
these are ideal, ideal components.
That means these things are mathematical perfect things
that we have in our minds that we're gonna try to build
in the real world but we'll come close.
We'll come very close.
We now have a wonderful set of equations:
V equals iR,
i equals C, dv, dt.
v equals L, di, dt.
These are gonna be like poetry for you pretty soon
and these ideal equations will produce
all kinds of really cool circuits for us.