How Electricity Actually Works

Summary

In this thought-provoking video, Derek Muller of Veritasium revisits the concept of electric circuits, addressing misconceptions about how energy is transferred through a wire. He clarifies that electrons do not carry energy from the battery to the bulb but are accelerated by an electric field created by charges on the battery and the wire's surface. Using a scaled-down model circuit and expert insights, Muller demonstrates that the bulb lights up almost instantly when the switch is closed, contrary to the initial belief that it would take a light-second. The video challenges traditional teaching methods and encourages a deeper understanding of the role of electric fields in circuit operation.

Takeaways

• 🔌 The video script discusses a thought experiment involving a large circuit with long wires and a light bulb connected to a battery and switch, aiming to clarify misconceptions about how electricity works.
• 🚫 The initial claim that light would appear from the bulb in 1/c seconds after closing the switch was deemed incorrect, as it implies faster-than-light communication, violating causality.
• 🔬 The script introduces a scaled-down model of the circuit to observe the behavior of the circuit in the first 30 nanoseconds, using fast scopes provided by Caltech.
• 🤔 It addresses common misconceptions about electricity, such as electrons carrying energy from the battery to the bulb or pushing each other through the circuit.
• 🌐 The script explains that the electric field, not the movement of electrons, is responsible for energy transfer in a circuit, with the field being created by charges on the battery and the surface of the wires.
• 🔋 The battery's role is likened to a shepherd, with surface charges acting as sheep dogs that guide the electrons (sheep) through the circuit.
• 📚 The importance of understanding surface charges in electric circuits is highlighted, with a reference to the book 'Matter and Interactions' by Chabay and Sherwood for further reading.
• 🛠️ The script uses the analogy of a transmission line with capacitors and inductors to model the circuit more accurately, emphasizing the role of fields in energy transfer.
• 💡 The experiment conducted in the video demonstrates that a visible light is emitted from the circuit's load (a resistor standing in for a light bulb) within nanoseconds of the switch being closed.
• 🤓 The video concludes by emphasizing that while voltage and current are convenient for circuit analysis, the actual carriers of energy are the electric and magnetic fields.
• 🌟 The script appreciates the community's engagement and the contributions of electrical engineering experts in clarifying and expanding upon the concepts presented in the video.

Q & A

What was the central topic of the video about the gigantic circuit?

The central topic of the video was to address the misconceptions and confusion surrounding the time it takes for light to appear from a light bulb in a circuit with extremely long wires, and to explain the actual physics behind the electric field and current flow in such a scenario.

What was the incorrect claim made in the original video that caused controversy?

The incorrect claim was that the light from the light bulb would appear after 1/c seconds, where c is the speed of light, which implies faster-than-light communication, violating causality and common sense.

What is the role of the electric field in an electric circuit?

The electric field in an electric circuit is responsible for accelerating electrons, which then transfer energy to the load (e.g., a light bulb) through collisions with the lattice structure of the material. The electric field is created by charges on the battery and on the surface of the wires.

Why do electrons not carry energy from the battery to the bulb?

Electrons do not carry energy from the battery to the bulb because the energy they transfer to the lattice comes from the electric field, not from the kinetic energy they might have carried from the battery. The electric field accelerates the electrons before each collision.

What misconceptions about electric circuits were discussed in the video?

Three misconceptions were discussed: 1) Electrons carry energy from the battery to the bulb, 2) Mobile electrons push each other through the circuit, and 3) The electric field comes entirely from the battery.

How does the electric field in a wire get established?

The electric field in a wire gets established almost instantaneously when the battery is connected to the circuit. Charges rearrange themselves on the surface of the wires and the battery, creating a charge distribution that results in an electric field both inside the wires and in the space around them.

What is the difference between the lumped element model and the distributed element model in circuit analysis?

The lumped element model simplifies circuit analysis by assuming that all interactions are localized within discrete circuit elements like resistors, capacitors, and inductors. The distributed element model, on the other hand, accounts for the spread-out nature of the interactions, such as the effect of charges on one wire on another, and includes elements like capacitors and inductors distributed along the wires.

What is the characteristic impedance of a transmission line, and how is it calculated?

The characteristic impedance of a transmission line is the resistance to alternating current that a source would see when sending a signal down the wires. It is calculated as the square root of the inductance divided by the capacitance of the line.

How does the video demonstrate that the bulb lights up almost immediately after the switch is closed?

The video demonstrates this through a scaled-down model of the circuit and measurements using a scope, showing that a voltage and current many orders of magnitude greater than leakage current flow through the load almost immediately, in roughly the time it takes light to cross the one-meter gap.

What is the significance of the Poynting vector in the context of this video?

The Poynting vector, which is the cross product of electric and magnetic fields, indicates the direction of energy flow in an electromagnetic field. In the context of the video, it shows that energy is carried by fields, not electrons, and can go straight across a gap, highlighting the role of fields in energy transfer.

Why did the video creator feel the need to clarify the original video's content?

The video creator felt the need to clarify because the original video led to a lot of confusion and controversy among viewers, particularly regarding the speed at which the light bulb would light up and the underlying physics of electric circuits.

What is the role of surface charges in the electric field within a wire?

Surface charges on the wire contribute to the electric field inside the wire. They create a gradient of charge along the wire, which, together with the charges on the battery, results in an electric field that accelerates electrons and drives the current through the circuit.

How does the video address the concern about causality being violated by the original claim?

The video addresses the concern by explaining that the bulb lights up due to the electric field it experiences, regardless of whether the circuit is complete or not. This means that the bulb's response is not dependent on the status of the entire circuit, thus not violating causality.

What is the purpose of the thought experiment involving a gigantic circuit with light-second long wires?

The purpose of the thought experiment is to challenge conventional thinking about electric circuits and to reveal the fundamental role of electric fields in energy transfer and current flow, which is often obscured by the more familiar concepts of voltage and current.

Outlines

00:00

🔌 Misunderstandings in Electric Circuits

This paragraph addresses misconceptions about how electric circuits work, particularly focusing on a thought experiment involving a large circuit with long wires and a light bulb. The creator admits that his previous explanation was misleading and clarifies that electrons do not carry energy from the battery to the bulb, nor do they push each other through the circuit. Instead, an electric field accelerates electrons, which then transfer energy to the filament upon collision, causing it to glow. The paragraph also corrects the idea that the electric field is solely from the battery, explaining that it's also influenced by charges on the wire's surface. The goal is to clear confusion and set the stage for a deeper understanding of electric fields in circuits.

05:00

🌐 The Role of Electric Fields in Circuits

This section delves into the true source of the electric field in a circuit, debunking the notion that electrons push each other through the wire. It explains that the electric field originates from both the battery and the charges on the circuit's wire surfaces. The paragraph uses an analogy comparing the battery to a shepherd, surface charges to sheep dogs, and mobile electrons to sheep, illustrating how the electric field guides electrons. It also discusses the establishment of surface charges almost instantaneously and the continuous work done by the battery to maintain them. The importance of understanding this concept is emphasized for analyzing circuits accurately, including the use of a simulation to visualize the electric field and energy flow, highlighting that energy is carried by fields, not electrons.

10:02

🚀 The Propagation of Electric Fields in a Large Circuit

The paragraph explores the implications of electric field propagation in a large circuit, such as the one described in the thought experiment. It explains how, upon closing the switch, the electric field inside the conductor is no longer zero, allowing current to flow. The change in the electric field travels at the speed of light, causing the light bulb to light up in 1/c seconds. The paragraph also addresses the simulation by Ben Watson, which demonstrates the electric field radiating out and generating current upon reaching the far wire. The focus is on showing that the electric field, not the changing magnetic field, is responsible for creating the current through the load. The discussion also touches on the concept of causality and how the灯泡 lights up regardless of the circuit's completeness, maintaining the integrity of physical laws.

15:02

🛠️ Advanced Circuit Analysis with Distributed Elements

This section introduces a more complex way of analyzing circuits using the distributed element model, which accounts for the effects of charges on one wire influencing another through capacitors, and the significant magnetic fields around long wires, modeled with inductors. The paragraph discusses the concept of characteristic impedance, which is crucial for maximizing power delivery to a load. It also presents experimental results, showing that a measurable voltage and current flow through the load almost immediately after the switch is closed, contrary to what was doubted in the previous video. The results are visualized with a graph, demonstrating that the signal is well above the noise level, and that the transferred power is sufficient to produce visible light, even with the wires being a meter apart.

20:04

💡 The Significance of Electric Fields in Circuit Education

The final paragraph reflects on the importance of understanding electric fields in circuit education and practice. It emphasizes that while voltage and current are convenient for circuit analysis, the real carriers of energy are the electric fields. The creator expresses excitement about the response to the video, particularly from electrical engineers who provided deeper insights into the subject. The paragraph also highlights the value of thought experiments in revealing underlying principles that are often overlooked. The video concludes with a sponsorship acknowledgment for Brilliant, an educational platform that encourages deep thinking in various scientific fields, and an invitation for viewers to explore its courses on electricity and magnetism.

Keywords

💡Circuit

A circuit is a closed loop that allows electric current to flow. In the video, the concept of a 'gigantic circuit' with light-second long wires is used to explore the propagation of electric signals. The circuit's design and components are central to the video's theme of how quickly electricity can illuminate a light bulb, demonstrating the foundational principles of electrical engineering.

💡Light-Second

A light-second is a unit of distance that represents the distance light travels in one second in a vacuum, approximately 299,792 kilometers. The video uses the term 'light-second' to describe the length of the wires in the hypothetical circuit, emphasizing the scale and the time it takes for the electrical signal to propagate through the circuit.

💡Electric Field

An electric field is a field that surrounds electrically charged particles and exerts force on other charged particles within the field. The video explains that electrons are accelerated by the electric field, not by pushing each other, and that the field is generated by charges on the battery and the surface of the wires, which is crucial to understanding how energy is transmitted in a circuit.

💡Ohm's Law

Ohm's Law is a fundamental principle in electrical engineering stating that the current through a conductor between two points is directly proportional to the voltage across the two points. The law is mentioned as a simplification of the complex interactions of charges and fields, illustrating how voltage, current, and resistance are related in a circuit.

💡Lumped Element Model

The lumped element model is an approach in electrical engineering that simplifies the analysis of circuits by treating components as if they are concentrated at a single point in space. The video contrasts this model with the more complex distributed element model, which accounts for the effects of fields and inductance along the wires, to explain the rapid propagation of electrical signals.

💡Surface Charges

Surface charges refer to the excess or deficiency of electric charge on the surface of a conductor. In the video, surface charges are highlighted as essential in establishing the electric field within a circuit. They are responsible for the rapid setup of the electric field when the circuit is energized, which is a key point in the discussion of signal propagation speed.

💡Poynting Vector

The Poynting vector is a quantity in electromagnetism that represents the directional energy flux density of an electromagnetic field. The video uses the concept of the Poynting vector to illustrate how energy is carried by the fields in a circuit, not just through the wires, which challenges the traditional view of energy transmission in circuits.

💡Transmission Line

A transmission line is a specialized type of electrical circuit that carries radio frequency or microwave signals. The video discusses the concept of a transmission line in the context of the gigantic circuit, using it to explain how signals propagate through the circuit and the role of inductance and capacitance in this process.

💡Distributed Element Model

The distributed element model is a more detailed approach to circuit analysis that considers the effects of inductance, capacitance, and resistance distributed along the length of the conductors. The video contrasts this model with the lumped element model to explain the behavior of the gigantic circuit and the speed at which the light bulb receives energy.

💡Characteristic Impedance

Characteristic impedance is the resistance to alternating current (AC) that a source would see when sending a signal down a transmission line. The video mentions calculating the characteristic impedance of the circuit to maximize power transfer to the load, which is an important concept in understanding how signals travel through the circuit.

💡Leakage Current

Leakage current is a small current that flows in a circuit even when the main switch is off. The video discusses the concept of leakage current to emphasize that the current flowing through the load when the switch is closed is significantly greater than this small background current, which is an important point in the debate about the speed of electricity in the circuit.

Highlights

A video was made about a gigantic circuit with light-second long wires and a light bulb just one meter away from the battery and switch.

The initial claim that it would take 1/c seconds for light to appear from the bulb after closing the switch was deemed incorrect.

The video sparked controversy suggesting communication could be faster than the speed of light, violating causality.

A scaled-down model of the circuit was used to observe the first 30 nanoseconds of activity with Caltech's fast scopes.

Richard Abbott from LIGO contributed to the experiment, emphasizing the importance of the magnitude of the voltage.

Misconceptions about electrons carrying energy from the battery to the bulb were clarified.

The role of the electric field in accelerating electrons and transferring energy to the lattice was explained.

The myth that electrons push each other through the circuit was debunked.

The origin of the electric field was explained as coming from both the battery and charges on the surface of the wires.

The speed of the setup process for surface charge distribution is limited only by the speed of light.

An analogy was provided comparing the battery to a shepherd, surface charges to sheep dogs, and mobile electrons to sheep.

The video demonstrated that energy in a circuit is carried by fields, not electrons, contradicting common misconceptions.

The concept of characteristic impedance in transmission lines was introduced and its calculation was explained.

Experiments showed that a visible light was produced even with a meter-long gap between the switch and the bulb.

The video concluded that current flows through the load almost immediately after the electric field reaches it.

The thought experiment aimed to reveal the normally hidden role of fields in electric circuits, challenging traditional teaching methods.

The video encouraged viewers to learn more about electricity and magnetism through interactive courses like those on Brilliant.

Transcripts

I made a video about a gigantic circuit

with light-second long wires

that connect up to a light bulb,

which is just one meter away from the battery and switch,

and I asked you, after I closed the switch,

how long will it take for us to get light

from that light bulb?

And my answer was 1/c seconds.

- And his answer is wrong.

- We would be able to communicate

faster than the speed of light.

- That violates causality and common sense.

- This is actually a bit misleading.

- Misleading.

- Misleading in a way.

- Extremely unconvinced.

- Naughty Mr. Veritasium has stirred up a right hornet's nest.

- Clearly I did not do a good job of explaining

what was really going on in the last video.

So I wanna clear up any confusion that I created.

So behind me, we have a scaled down model of this circuit.

It is only 10 meters in length on either side.

Obviously that's a lot shorter than one light-second,

but for the first 30 nanoseconds,

this model should be identical to the big circuit,

and Caltech has very fast scopes,

so we'll be able to see what's going on in this time.

I got a ton of help on this from Richard Abbott,

who works on LIGO, the gravitational wave detector.

Over here, we are going to put a little resistor,

which is gonna be the stand in for our light bulb,

and we're going to measure it with a scope and see essentially,

what is the time delay between applying a pulse

on the other side, basically flicking the switch,

for us to get a voltage across our resistor.

And the magnitude of that voltage is really important.

A lot of people thought it would be negligible.

- The amount of energy supplied by this is so minuscule.

- A tiny, tiny effect, right?

- The amount of power you're getting

to the lamp over here, it's nuff-all

- He meant the light turns on

at any current level immediately.

- That is not what I meant.

- Well, actually, with that assumption,

Derek's answer is wrong.

The light never turns off

no matter the state of the switch.

Some electrons will jump the gap and result in an extremely

small continuous leakage current.

- Let me be clear about what I am claiming.

Okay, it is my claim that we will see voltage

and current through the load that is many orders

of magnitude greater than leakage current,

an amount of power

that would actually produce visible light

if you put it through an appropriate device,

and we will see that power there

in roughly the time it takes the light

to cross the one meter gap,

but to understand why this happens,

we first have to clear up some misconceptions

that I saw in responses.

Misconception number one is thinking that electrons

carry the energy from the battery to the bulb.

Let's say we have a simple circuit with a battery and a bulb

operating at steady state.

If you zoom in on the light bulb filament,

you'd see a lattice of positively charged cores of atoms,

the nucleus and lowest shells of electrons,

surrounded by a sea of negative electrons,

which are free to move around the lattice.

The actual speed of these electrons is very fast,

around a million meters per second,

but all in random directions.

The average drift velocity of an electron

is less than 0.1 millimeters per second.

Now frequently, an electron will bump into a metal ion,

and transfer some or all of its kinetic energy

to the lattice.

The electron slows down and the metal lattice

starts wiggling more.

It heats up.

And ultimately this is what causes the filament

to glow and emit light.

So a lot of people will look at this and conclude

the electron carried the energy from the battery to the bulb

where it dissipated its kinetic energy as heat,

but consider, where did the electron get its kinetic energy

from before the collision?

It didn't carry that energy from the battery.

In fact, if the circuit has only been on for a short time,

that electron hasn't been anywhere near the battery.

So how was it accelerated before the collision?

The answer is, it was by an electric field in the wire.

The electron repeatedly collides with the lattice,

and loses energy.

And after each collision,

it is again accelerated by the electric field.

So although it is the electron that transfers energy

to the lattice, the energy came from the electric field.

So where does that electric field come from?

Well, a lot of animations make it look like the electrons

push each other through the circuit

via their mutual repulsion.

So you might think the electric field

comes from the electron behind it.

There is the analogy of water flowing through a hose,

or marbles in a tube.

This is misconception two, thinking that mobile electrons

push each other through the circuit.

That is not how electrons flow in circuits.

The truth is if you average over a few atoms,

you find the charge density

everywhere inside a conductor is zero.

The negative charge of electrons and the positive cores

of atoms perfectly cancel out.

So for each repulsive force between electrons,

there is an equal and opposite force from the positive ion

next to it.

These forces cancel out.

So mobile electrons cannot push each other through the wire.

So where does the electric field come from?

Misconception number three is that it comes

entirely from the battery.

This makes intuitive sense,

since the battery is the active element in the circuit,

it has a positive side and a negative side.

So it has an electric field,

but this is not the electric field that all the electrons

within the wire experience.

Consider that the electric field

of the battery is much larger close to the battery.

So if its field were really what's pushing

the electrons around,

then if you brought the light bulb close to the battery,

then the bulb would glow much brighter.

And it doesn't.

The truth is that the electric field in the wire

comes both from the battery and from charges

on the surface of the wires of the circuit.

As you go along the wire from the negative end

of the battery to the positive end,

there is a gradient of charge built up on its surface,

starting with an excess of electrons,

through to roughly no charge in the middle,

as we'll see the steepest charge gradient is actually

across the load to a deficiency of electrons,

the exposed positive cores of atoms on the surface

of the positive end of the wire.

All these charges and the charges on the battery

create the electric field everywhere inside the wires.

They also create an electric field

in the space around the wires.

These surface charges were set up almost instantaneously

when the battery was inserted into the circuit.

You might think you'd have to move electrons

a significant distance to create this charge distribution,

but that is not the case.

Even a slight expansion or contraction of the electron sea,

with electrons moving on average, the radius of a proton,

can establish the surface charges you see.

So the time for the charges to move

is completely negligible.

The speed of the setup process is limited

only by the speed of light.

Once that surface charge distribution has been established,

the battery does continuous work to maintain it,

by moving electrons through the battery

against the Coulomb force.

In the load, the electric field

created by all the surface charges, accelerates electrons,

which dissipate their energy in collisions with the lattice.

So the battery is putting energy into the field,

which electrons take out and transfer to the load.

An electrical engineer who made a response video,

Ben Watson, came up with a good analogy.

The battery is like a shepherd.

The surface charges are the sheep dogs

responding to his orders.

And the mobile electrons are the sheep,

guided by those barking dogs.

The surface charge description of electric circuits

is omitted from most textbooks,

but there is a great treatment of it

in Matter and Interactions by Chabay and Sherwood.

They also have a VPython simulation where you can see

the positive surface charge in red,

and negative surface charge in blue.

You can see how this entire charge distribution

creates a net electric field shown by the orange arrow,

everywhere in and around the circuit,

everywhere inside the wire,

the electric field has the same magnitude

and its direction is along the wire.

This is really showing you the electric field

in the center of the wire, but it's depicted on the surface

so you can see it.

In this circuit,

all the conductors are made of the same material,

but the segment at the bottom

has a much narrower cross section.

So it represents a resistor.

Since the cross sectional area is smaller,

the electron drift velocity through the resistor

has to be higher so that it can carry the same current

as everywhere else in the circuit.

Now, drift velocity is directly proportional

to electric field.

So the electric field must be largest inside the resistor.

And this is achieved by having the steepest gradient

of surface charges here.

You can also see the contribution to the net electric field

from the battery in magenta,

and the contribution from surface charges in green.

Far from the battery,

most of the electric field is due to surface charges,

whereas close to the battery, it has a greater contribution

and the field due to surface charges

is actually in the opposite direction

to the field from the battery.

So to sum up, electrons don't carry the energy

from battery to bulb,

nor do they push each other through the wire.

They are pushed along by an electric field,

which is created by charges on the battery,

and charges on the surface of the wires.

With this view of circuits,

things that might have previously seemed mysterious,

make a lot more sense.

Like if electrons leave a battery at the same rate,

and with the same drift velocity as they return,

how do they carry energy from the battery?

The answer is they don't.

They are accelerated by the electric field

before each collision with the lattice.

At a junction, how do the correct number of electrons

go down each path?

Well, they're guided by the electric field,

which extends everywhere throughout the circuit.

The fields are the main actors,

extending everywhere throughout the circuit,

and the electrons are just their pawns.

So how does this apply to the big circuit?

When the battery is connected into the circuit,

even with the switch open, charges rearrange themselves.

On the negative side of the battery,

there is an excess of electrons

on the surface of the wires and the switch.

On the positive side, there is a deficiency of electrons.

So positive charges built up on the surface of the wires.

The charges rearrange themselves until the electric field

is zero everywhere inside the conductor.

This electric field is due to all the surface charges

and the charges on the battery.

There is an electric field outside the wires

due to these charges, but it's zero inside the wires.

We now have the full potential difference

of the battery across the switch.

And no current is full flowing, except for leakage current,

which I'll assume is negligible.

When we close the switch,

the surface charges on both sides of the switch

neutralize each other on contact.

And at that instant,

the electric field inside the conductor is no longer zero,

and current starts flowing through the switch.

Simultaneously, the new electric field

from the modified surface charges

radiates outwards at essentially the speed of light.

And when it reaches the bulb,

the electric field inside it is no longer zero.

So current starts to flow here too.

This is why I said the bulb lights up in 1/c seconds,

because the bulb was one meter from the switch,

and the change in the electric field travels out

at the speed of light.

As some of you pointed out,

the answer should have been one meter divided by C.

And I apologize for the casual use of units.

If you were to move the switch,

then the bulb would take

a different amount of time to emit light,

which just depends on the distance

between the switch and the bulb.

In response to my original video,

Ben Watson simulated a model of the circuit

using software from Ansys called HFSS.

It provides a complete solution to Maxwell's equations

in three dimensions.

Now have worked with Ben and Ansys

to make these simulations.

When the switch is closed,

you can see the electric field radiate out,

and as it hits the far wire, it generates current.

The electric field is to the right.

So the electrons flow to the left.

This simulation shows the magnitude of the magnetic field,

which falls off pretty rapidly as it crosses the gap.

But then a magnetic field appears around the far wire,

and this magnetic field is created

by the current in that wire.

To me, this suggests that it really is the electric field,

and not the changing magnetic field

that creates the current through the load.

Some commenters on the original video

claimed my answer of three or four nanoseconds

violates causality.

I guess they were thinking that the bulb

would only go on if the circuit were complete.

And it wouldn't if the circuit were broken somewhere,

which could be up to half a light second away.

So it seemed like I was saying,

we could get information about the status

of the whole circuit, even half a light second away,

in just nanosecond seconds.

But that is not what I was saying.

What I should have stated explicitly,

is that the bulb goes on

regardless of whether the circuit is complete or not.

The current flows through the load

due to the electric field it experiences.

To illustrate this, Ben added a wire below the circuit

that is completely disconnected from it.

You can see is that its response

to the changing electric field is virtually identical

to that of the top wire,

at least up until the signal reaches the far end

and reflects back.

This is why my answer doesn't break causality.

At least initially, connected and disconnected wires

behave exactly the same.

Using this software,

you can also simulate the Poynting vector

that is the cross product of electric and magnetic fields.

In the last video, I showed how the Poynting vector

indicates the direction of energy flow.

And after the switch is closed,

the Poynting vector points out of the battery,

across the gap to the other wire, whether connected or not,

because energy is carried by fields and not electrons,

it can go straight across the gap.

So you might ask, why do we need wires at all?

Well, we don't, I mean, phones and toothbrushes

charge without wires connecting them

to a stream of electrons,

and researchers have demonstrated remote charging

using the energy from WiFi signals.

Wires are more efficient because they channel the fields

and hence the energy from source to load.

Here's another angle on the Poynting vector.

And you can see once there is current in the top wire,

the fields around it carry energy in both directions.

Now, of course, the Poynting vector also points

parallel to the first wire,

carrying the energy around the circuit

as most people would expect.

But again, note how the energy is carried outside the wires,

not in the wires.

Now admittedly, thinking about circuits this way

is complicated.

And since nobody wants to solve Maxwell's equations

in three dimensions just to analyze a basic circuit,

scientists and engineers have worked out shortcuts.

For example, Ohm's law,

voltage equals current times resistance,

is just the macroscopic result of all the surface charges,

their electric fields and zillions of electrons

bumping into zillions of metal ions.

You can simplify all that physics

into a single circuit element, a resistor,

and the basic quantities of current and voltage.

This is called the lumped element model,

lump all the spread-out multi particle and field

interactions into a few discrete circuit elements.

And we use this technique

every time we draw a circuit diagram.

So our original diagram of the big circuit is flawed

because fields between the wires

are important to the problem,

but there are no circuit elements

to indicate these interactions.

To fix it, we need to add capacitors all down the wires.

These capture the effect charges on one wire

have on the other.

If there are negative charges on the surface

of the bottom wire, for example,

they'll induce positive charges

on the surface of the top wire.

Also, since these wires are long,

they're gonna create significant magnetic fields

around them, which resist changes in current.

So we model this with inductors all the way down the wires.

We could also add resistors,

making what electrical engineers would recognize

as the distributed element model for a transmission line.

But we're assuming that these wires are super conducting.

So this is how we could model

a super conducting transmission line.

This diagram offers another way of understanding

why current flows through the load almost immediately.

When you first apply a voltage across a capacitor,

current flows as opposite charge builds up

on the two plates.

In the short time limit, a capacitor is a short circuit.

It acts just like an ordinary wire.

Once it's charged up, no more current flows,

but by this point, the next capacitor is charging up.

And then the next one, and then the next one.

And so we have a loop of current that is expanding out

at roughly the speed of light.

This is of course, just another way of talking

about the effect the electric field

that the bottom wire has on the top wire.

One reason it's useful to look at the circuit this way,

is because you can use the values of inductance

and capacitance to calculate the characteristic impedance

of the transmission lines.

You can think of this as the resistance

to alternating current that a source would see

when sending a signal down the wires.

The characteristic impedance is equal to the square root

of inductance divided by capacitance.

And for our circuit,

I measured the capacitance and the inductance of the lines,

- 11.85, call it, micro Henry's.

- So we got a characteristic impedance of about 550 Ohms.

To maximize the power delivered to our load,

we want its resistance to equal the sum of the other

impedances in the circuit.

So that's why we picked a 1.1 kilo-Ohm resistor.

Now, I hope you're convinced that current will flow

as soon as the electric field reaches the far wire.

The question is, how much?

Are we gonna see an appreciable voltage

even with these lines a meter apart?

That's what it seemed like a lot of people were doubting

in the last video.

So that's really what we want to find out here.

Okay, so now we're putting a pulse in there.

- Yep.

Well looky, looky, Derek.

- So what do we got that yellow one is our-

- Got a fraction of the applied voltage overshoot.

And then-

- So it looks to me like the initial voltage

that we're getting is about-

- Five volts per division.

So it looks like about five volts,

roughly four or five volts.

- The green curve rising up to around 18 volts

is the source voltage.

And the yellow line is the voltage across the resistor.

So after just a few nanoseconds,

this voltage rises to around four volts.

Since the resistor was a kilo-Ohm,

that means four milliamps of current

are flowing in the resistor,

before the signal goes all the way around the circuit.

So we were transferring about 14 milliwatts of power.

This is what 14 milliwatts of light actually looks like.

So, yeah, it's not a fully on bulb,

but it is visible light and way more than you would get

from just leakage current.

Now, some of you may argue,

it's unfair to use a little LED when I showed a bulb

and car battery in the original video,

but those items were for illustrative purposes only.

The clue that this is actually a thought experiment

is the two light-seconds of super conducting wire

that stretch out into space.

This is not an engineering question about how best

to wire up a light bulb in your bedroom.

The question was intentionally vague.

And if you want to choose circuit components

such that the bulb never goes on,

you are welcome to do that

and I support your conclusion.

Just to me, the most interesting way

to approach this problem is to ask,

how could you make the light go on fastest?

I was worried that those long wires would pick up

all the radio waves passing through,

and we wouldn't even be able to see

the signal for that noise,

but you can see clearly on the graph

that the signal is way above the noise level.

Alpha Phoenix set up a kilometer of wire

and got a very similar result.

- So the light bulb turns on a little bit,

and then after one light-speed delay,

the light bulb turns on the rest of the way.

- YouTuber, ZY, simulated the transmission line circuit,

and found that even with realistic assumptions,

he transferred 12 milliwatts to the load straight away.

- Derek is actually more correct

than we give him credit for.

So, I believe that he's correct on all counts.

And the question is neither deceptive

or requires like technicalities.

- So everyone agrees that a steady, small,

but way-bigger-than-leakage-current signal

flows through the load in the first second

after the switch is closed.

Is it enough to emit light?

Yes, if you use an LED.

But the point of the thought experiment

was to reveal something that's normally hidden

by the way that we think about and teach electric circuits.

You know, we use voltage and current and lumped elements

because they're more convenient

than working with Maxwell's equations,

but we shouldn't forget that the main actors

are actually the fields.

They are what carry the energy,

and you don't have to take my word for it.

This is Rick Hartley,

a veteran printed circuit board designer.

- I used to think in terms of voltage and current.

And I used to think that the energy in the circuit

was in the voltage and current, but it's not.

The energy in the circuit is in the fields.

The most important thing you need to know

is that when you route a trace,

you better define the other side of that transmission line,

because if you don't, those fields are gonna spread

and they're gonna leave you an unhappy individual.

- I think one of the things that I'm most excited

about the circuit's video was the response videos

I saw by so many people,

especially people with far better credentials

in electrical engineering than me.

I really enjoyed watching those videos.

So I feel like my circuits video was kind of like,

a mistake on my part in certain ways

that I didn't delve deep enough

into this part of the problem.

I honestly didn't think that this

was the focus of the video,

but clearly everyone who watched it did, so that's on me,

but by making that mistake,

and by not going deep into my explanation,

I invited seemingly a whole bunch of other people

to make explanations, which I thought were great.

And some people like Alpha Phoenix even took up

the challenge and set up his own version of the experiment.

So, frankly, I'm just really excited at what came about,

even though I do acknowledge that this was my fault

in the first place.

Like I should have done a better explanation,

but by not doing so, you know,

there are a lot of great explanations out there.

And that's what I love.

So I'm gonna recommend a whole bunch

of electrical engineering YouTubers to you

in case you wanna check those out

because they're a lot of great channels,

and you should really see how they think about electronics,

and how they explain this circuit.

Hey, this video was sponsored by Brilliant,

the website and app that gets you thinking deeply

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Brilliant is sponsoring a lot of our videos this year,

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And they have a great course on electricity and magnetism,

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I really think this is the best way to learn

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The difficulty builds gradually.

And by asking you questions,

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If you need help,

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You know what sets Brilliant apart is their interactivity.

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