Lesson video

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Hello, my name's Dr.

George.

This lesson is called Resistance of Hot Metal, and it's about understanding how filament lamps behave, as part of the unit circuit components.

The outcome for the lesson is "I can explain why the resistance of a metal filament changes as the p.

across it increases.

And here are the key words, which I'll be introducing as we go along.

If you need to remind yourself of the meanings later, you can come back to this slide.

The lesson has two parts called resistance of a filament lamp and resistance of the metal ion lattice.

When the current in a filament lamp increases the glowing filament, the twisted wire inside, becomes hotter and brighter.

This graph shows how the current varies as the p.

across the lamp varies, and here's what happens with the resistance as well.

With low p.

, the current is low and the resistance is low, and the lamp is not very bright.

When the p.

increases, not surprisingly, the current increases.

The p.

determines the size of the push on the electrons, but also the resistance increases.

And at high p.

the current is high and the lamp is bright and the resistance is also high.

So which of these images most accurately shows the appearance of the filament lamp at a low p.

d? And when I ask you a question, I'll wait for five seconds, but you may need longer, in which case, press pause while you choose your answer and press play when you're ready.

And the answer is A, at low p.

the current is also low and the lamp is not very bright, and we're in the region of the graph circled here.

Now a resistor is different.

The current through a resistor at a constant temperature is directly proportional to the p.

across it.

So the graph of current against p.

looks like this.

And when a component behaves like this, we call it an ohmic conductor.

Now the temperature has to stay the same, but under certain conditions, the temperature of resistor can stay roughly constant, in which case is resistance is roughly constant.

And that's why you can say this resistor is a 12 ohm resistor, for example.

it has a fairly consistent resistance.

Whereas the resistance of a filament lamp changes as the p.

and the current change.

And that's why its graph is not a straight line.

We say it's a non-ohmic conductor.

So current proportional to p.

, ohmic conductor, and not proportional, is a non-ohmic conductor.

Which of the graphs below was produced by an ohmic conductor? And if you remembered correctly, it's B, it's a conductor in which current is directly proportional to p.

So we would expect that graph to be a straight line that passes through the origin.

You can find the resistance of a component from a graph of current against p.

using values that you read from the graph for the current and the p.

For example, at a p.

of 2.

0 volts, we can read that the current is 0.

3 amps, as shown on the graph.

And resistance of a component is the p.

across it divided by the current through it.

So doing that calculation, we get to two significant figures, 6.

7 ohms for the resistance of this component.

Let's look elsewhere on the graph and do the calculation again at a p.

of 3.

0 volts, we can read a current of 0.

45 amps.

So calculating V divided by I, We get 6.

7 ohms again.

And a third time, 5.

0 volts, we have a current of 0.

75 amps.

You can see that from the graph and calculating resistance, 6.

7 ohms. And that's what we get when we have an ohmic conductor.

When we have a straight line graph like this, we find that the resistance is the same at every value of p.

and current.

So that's for an ohmic conductor, and that would include resistors as long as the temperature remains constant.

Which of the following statements about an ohmic conductor at a constant temperature is correct? Press pause while you read these and press play when you've chosen your answer.

Correct answer is the resistance remains constant as the p.

increases.

Now we can also say that resistance of a component is related to the gradient of a graph of current against p.

You can use this when you're looking at resistors.

This resistor has a low resistance.

There's quite a high current flowing a given p.

at least compared with this resistor, which has a higher resistance because there's a lower current flowing for a given p.

So for a particular value of p.

d, the upper resistor has a higher current flowing through it, so it has a lower resistance.

Which of the lines on this graph represents the lowest resistance? The answer is A.

We have for the same p.

the highest current in resistor A.

So it has the lowest resistance.

Well done if you picked that one.

So a resistor in a filament lamp behave differently when the p.

across them is increased.

Here's both of them on the same graph.

At low p.

they have similar behaviour, and these two components happen to have similar resistance at low p.

Their graphs almost overlap, but the grafts become much more different at a higher p.

At higher p.

, less current flows in the lamp for the same p.

because its resistance is now higher than the resistors.

So as the p.

increases, the resisters resistance is staying the same, but the lamp's resistance is increasing.

The behaviour of a resistor and filament lamp is the same when the p.

across them is applied in the opposite direction.

So if you switch the connections to the battery or power supply, they behave in the same way.

That's not true for all types of component, but it's true for these.

So on the left we have the resistor, ohmic conductor, straight line graph.

On the right we have the filament lamp, non-ohmic conductor, and the graph is not a straight line.

Which of these graphs shows how a filament lamp behaves when a range of different p.

are applied across it? And you saw this on the previous slide.

It looks like this.

And now some written questions for you.

You'll need to press pause while you read these and write down your answers and press play when you're ready to check them.

So I'll show you some example answers.

First, you are asked to describe how the currency resistors changes as the p.

across them increases.

And here's a way that you could answer that.

As the p.

increases across each resistor, the current through it increases.

When p.

doubles, current also doubles.

So the current is directly proportional to the p.

The important thing is to get the idea that as one increases the other increases in a directly proportional way.

Then explain how the graph shows that one resistor has a higher resistance than the other.

The current increases less in resistor B than in resistor A for the same increase in p.

showing that resistor B has a higher resistance.

And now describe how current through the filament lamp changes as the p.

across it increases.

You could say, as the p.

increases, the current through the lamp also increases.

at low p.

values the current rises rapidly.

However, as the p.

becomes larger and continues to increase, the current increases more slowly.

You see that here on the graph, current increasing rapidly and then more slowly.

And finally, you were asked to explain what happens to the resistance of the filament lamp.

As the p.

across it increases.

As the p.

increases, the current rises more slowly because the lamps resistance increases.

This makes it harder for the additional p.

to push more current through the lamp.

So well done if you've got most or all of those right.

And now we're going to move on to the next part of the lesson, resistance of the metal ion lattice.

We're gonna look at why does a filament lamp behave in this way, why does its resistance increase as the current increases? To do that, we need to know what a metal is like microscopically.

Here's a simplified model of a metal ion lattice.

So this is a regular arrangement of metal ions and ions are atoms that have gained or lost electrons.

So the ions in a metal have actually lost some of their electrons, some of their outermost electrons that leaves them positively charged.

And in a solid, the atoms or for a metal, the ions vibrate, but they're held in fixed positions.

They can't swap places with each other.

Now, the electrons that those ions have lost are distributed through the lattice.

They're called free electrons because they're able to move from ion to ion so they can travel through the metal.

Now a recap.

How do free electrons and metal ions behave? Press pause while you read these and choose your answers.

Well, the correct options are B, the metal ions vibrate, move backwards and forwards, and the free electrons can move from ion to ion.

And here's the model again, but with more detail added, we can see that the ions are positively charged and the lines around them represent that they're vibrating.

And the free electrons, the lines behind them, represent that they're moving around.

And as the free electrons move around, they collide with the ions.

And when they do that, they make the ions vibrate more vigorously, more energetically.

So which is the best model here for metal ions and free electrons? Some of them look very similar to each other, but they are all slightly different.

Did you pick C? C shows the ions vibrating, and it also shows that the electrons, the free electrons are moving around.

B and D are missing the vibrations of the ions.

And D doesn't show the electrons properly at all, and A is missing the movement of the free electrons.

If we have a higher p.

across a piece of metal, across a wire, it causes the free electrons to be pushed through with a larger force, and that causes the free electrons to move faster.

And so they collide with the metal ions with more force and more often.

Imagine a slow moving free electron hitting an ion.

It's going to cause that ion to vibrate a little more vigorously, a little more energetically.

But now, if we have a fast moving free electron, colliding with the ion, it's going to make it vibrate a lot more vigorously when it collides.

Which of the following will cause a greater push on the free electrons in a metal? And it's the p.

that's associated with how strongly the electrons are pushed along the wires.

Now, in a solid, the particles are vibrating all the time.

So in a metal, the ions vibrate.

But if the metal is colder, the ions vibrate less vigorously and the free electrons move around less quickly compared with if the metal is hotter.

So when the temperature increases, we have more energetic vibration of the ions and the free electrons move faster.

Let's check if you're paying attention.

Which of the following statements describes what happens when a metal is heated? Correct answer is free electrons move faster and metal ions vibrate more vigorously Even at low temperatures, metal ions in a metal do vibrate, and when the p.

across the metal is increased, the free electrons move faster.

They collide with the metal ions more often and with more force and make the ions vibrate more vigorously.

And this makes the temperature of the metal increase.

So might start with a circuit in which everything, including the wires ,is at quite a low temperature.

But if you then apply a p.

using a power supply or a battery, the electrons flow around and the temperature of the metal is going to start to increase.

And that's because increasing the p.

across a metal increases the current flowing through it, and that causes more frequent collisions.

Resistance is caused by collisions between electrons and ions.

If there's more movement, there will be more collisions between the free electrons and the metal ions.

So if the ions vibrate more vigorously, there'll be more collisions sending the electrons off in different directions, and that reduces the current, it increases the resistance of the metal.

Which of the following causes electrical resistance in metals? And of course, it's free electrons colliding with metal ions.

The current itself is caused by the flow of free electrons in one direction, but the collisions of free electrons with the ions reduces the size of that current.

We can now explain the resistance of a filament lamp using the metal ion lattice model that we've just described.

At a low p.

the current is low, and there are a few collisions between electrons and ions.

Collisions don't happen as often.

And so we have low resistance.

At a higher p.

the current is higher, there are more collisions between electrons and ions.

The ions are vibrating more energetically and the resistance is higher.

Since the resistance of a filament lamp changes with p.

it increases as p.

increases.

We say it's not an ohmic conductor, it's a non-ohmic conductor.

This is what the graph would look like for an ohmic conductor, such as a resistor at constant temperature.

It's a straight line.

Here with three identical 12 volt lamps.

Which of the lamps shown here has the lowest resistance at the moment? And it's the dimmest lamp because the temperature of the filament is lowest in that lamp.

Now some questions for you, so press pause when you read these and write down your answers and press play when you finished.

Let's take a look at the answers.

So you were asked to sketch a graph for a filament lamp of current against p.

It's a curve of this sort of shape.

Question two, as the p.

across the filament lamp increases the current through the lamp, also increases.

Free electrons move faster, colliding more frequently and more forcefully with metal ions.

This causes the metal ions to vibrate more vigorously, raising the temperature of the metal until it glows white hot.

Take a look at your own answer and see if it has a clear structure, like this one, explaining one thing and then what that causes and what that causes.

And finally, when the metal filament in the lamp gets hotter, the metal ions vibrate more vigorously.

This makes it harder for free electrons to move through the metal without colliding, resulting in an increased resistance.

Well done if you're getting a lot of these right, and if you're not, you might want to go back and rewatch some of the earlier slides.

And we're at the end of the lesson now.

So here's a summary of what it included.

In a metal, metal ions are arranged in a regular lattice, while they vibrate they remain in fixed positions.

Electrons from the outer shells of atoms are distributed throughout the lattice and are known as free electrons because they can move from ion to ion.

When the p.

across a filament lamp increases, the current also increases.

The free electrons collide with metal ions more frequently and with greater force, causing the metal ions to vibrate more vigorously and making the metal hotter.

In a hotter metal, it becomes more difficult for free electrons to move past the metal ions, which increases the resistance of the metal.

Well done for working through this lesson, and I hope you now understand why a filament lamp behaves the way it does.

I hope to see you again in a future lesson.

Bye for now.

I've finished the video