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## Circuit elements

Current time:0:00Total duration:6:31

# Ideal circuit elements

## Video transcript

- [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.