Ideal circuit elements | Circuit analysis | Electrical engineering | Khan Academy

- [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.