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### Course: Electrical engineering > Unit 2

Lesson 1: Circuit elements# Ideal circuit elements

Explore the world of circuit analysis with the three fundamental circuit elements: resistors, capacitors, and inductors. Understand their unique symbols, properties, and the key equations that connect voltage and current for each component. Master Ohm's law for resistors, the capacitor equation, and the inductor equation to build a strong foundation in circuit design and analysis. These ideal component equations will unlock the door to creating and understanding a wide variety of electrical circuits. Created by Willy McAllister.

## Want to join the conversation?

- So I was looking through my EE notes from last semester and I see an inconsistency:

@7:26when you start labeling the Voltage sources direction for current you show that the direction of the current is into the source as opposed to out of the source! I verified with the textbook and for a voltage source the current points out from the positive terminal.(14 votes)- Depends how you want to look at the system. Conventional current (which I have been taught in college/high school classwork) does have current flow from the positive terminal, but the actual electron current flows from the negative to positive. I admit the conventional current is easier to work with in circuit analysis, but when I do electron flow models, I do have to use current flow coming out of the negative terminal.(40 votes)

- Why do we need a current source?

If we have a voltage source, current automatically flows, if the circuit is closed(12 votes)- Ideal constant voltage and constant current sources are mathematical conceptions. Both of them create both voltage and current. One keeps voltage constant, the other keeps current constant. In the real world, we are more familiar with voltage sources such as batteries or wall plugs. We build real-world voltage sources by packaging chemical reactions (batteries) or by driving generators with steam or falling water. A power supply (a complicated circuit) as another kind of source of constant voltages. There are plenty of real-world current sources, too. Constant current sources can be designed just like power supplies for constant voltage. Inside your cell phone, the analog amplifiers that send and receive the signals all have 2-transistor circuits called "current mirrors", which act as a current source. When we model a bipolar junction transistor (BJT), this transistor has a tiny current source inside.(11 votes)

- I didnt exactly understand what a capacitor does Can anyone please clarify??

Thanks in advance! :-)(5 votes)- Capacitor holds an electric charge so it can discharge it later.

It charges and discharges itself, basically.(12 votes)

- Is a solar panel a circuit?(6 votes)
- No, you can consider a solar panel as a voltage supply from the video above. It's an element to be part of a circuit and it supplies voltage to the circuit based on the amount of light it is receiving.(8 votes)

- what is the use of an inductor ?(7 votes)
- A use of an inductor is in a low pass filter. Also 2 inductors side by side makes a transformer.(1 vote)

- But what about an inverter? I know that with wind and solar power you produce DC and store it in batteries and if you want to have a much higher voltage AC(DC voltage is usually around 6 volts per solar battery whereas AC at home is usually around 100-200 volts) produced by the low voltage DC you need an inverter which is something that converts DC to AC and raises the voltage in the process.

How would you represent that in a circuit?(5 votes)- Inverters are much more complex circuits, designed using other types of circuit elements, including microcontrollers, gotta work up(3 votes)

- When are uppercase V and I used, and when lowercase v and i? I have noticed lowercases are often used with capacitors and inductors (when V and I they are not constant). Can anybody confirm this or am I wrong? If so, what is the difference?(2 votes)
- Hello Joost,

Confirmed!

As a rule the uppercase V and I are used for DC circuits. The lowercase v an i are used for time varying or AC circuits. In DC we talk about V and in AC we talk about v(t).

However, later in your studies you will be introduced to phasors and then once again we will see V and I except this time they are in bold face type.

Enjoy,

APD(6 votes)

- How would you create an operational amplifier with a gain of unity? I believe this is called a unity follower and am assuming no resistors would be required. How would you wire an oscilloscope to measure the input and output voltage?(3 votes)
- An op amp whose output feeds directly into its inverting (-) input will have a gain of 1 respective to the voltage at its non-inverting (+) input.

In an ideal op amp this configuration will always result in a gain of 1 regardless of the input voltage. In a real world component the output voltage may not be able to reach the same voltage as the non-inverting input. Due to for example power supply limits, if you power the op amp from +5V and 0V don't expect the output to be able to track the input above +5V or below 0V (or even to exactly +5V or 0V as the output of a real op amp can't reach to exactly equal to its power rails).

Also a real world op amp will not be able to provide a stable output in a unity gain configuration at all input frequencies. This is because there is a propagation delay from the input to the output.

Regarding an oscilloscope, a basic oscilloscope probe measures between two points the reference being the probe tip, with respect to the ground (usually a crocodile clip). If the scope has multiple channels the grounds of the probes will be connected together. This means that for the most part you can only measure voltages in your circuit with respect to 0V. To measure a unity gain op amp circuit, you would use one channel to measure the input with respect to ground (so the probe tip connected to the non-inverting input and the ground to 0V) and the second channel to the output in the same manner.(4 votes)

- what is the use of capacitor and inductor in a circuit ?(3 votes)
- Capacitors have two main jobs in a circuit.

When connected to signals that are changing, capacitors are used as filters. A filter allows some frequencies to pass through while other frequencies are discouraged.

When a capacitor is connected to a voltage that is supposed to remain steady (a power supply voltage for example), the capacitor acts as a reservoir or bucket to hold charge close to where it is needed.

Inductors are used in filters in a similar way as capacitors. This is becoming less common because inductors are invariably large objects. They are hard to fit inside modern gadgets. The other job for inductors is in power supply circuits that convert high voltage AC from a wall plug into low voltage DC used inside plug-in equipment like desktop PCs or monitors. When you see a power cord with a cylinder-shaped lump in it, that lump is a type of inductor (called a ferrite core).(2 votes)

- What's the difference between a component and an element?(2 votes)
- Element and component mean about the same thing. "Element" is the more theoretical term, like when you say "element voltage" (the voltage appearing across an element). I use "element" when I'm talking about everything in the circuit (resistor, capacitor, inductor, voltage source, current source). I use "component" when I'm talking about just a passive element (resistor, capacitor, inductor). Components come as individual little objects. Voltage and current sources are complicated things made of many parts, so they don't seem like "components" to me, but they are basic circuit elements.(1 vote)

## 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.