Hello, I'm Dr.

de Mello and I'll be teaching you today's lesson.

Today's lesson is about the length of a wire and it's from the resistance and parallel circuits unit.

The outcome we have today is, I can explain why longer wires have a higher resistance than shorter wires, let's begin.

There are four sets of keywords in today's lesson.

The first keyword is resistance.

This is the opposition to current that can flow in a circuit or through components.

The second sets of keywords are metal ion.

When a metal atom loses an electron, it becomes a positively charged iron.

Our third keyword is electron.

Electrons are negative charges that flow in circuits to create current.

Our last keyword is proportional.

Proportional is used to describe how variables are related to each other.

If one variable is proportional to another, they change as a constant multiple of each other.

Here are the keywords with their definitions.

If you like, pause the video now and read through them, but be sure to look out for them in the rest of the lesson.

This length of a wire lesson has two parts.

The first part is about current through wires of different lengths.

The second part looks at the resistance of wires of different lengths.

Let's begin with current through wires of different lengths.

A thin nichrome wire has a significant resistance compared to other metals and it opposes the flow of current.

The resistance is caused by the metal ion inside the wire.

One model of resistance is that an electron collides with metal ions as it moves through a wire.

This opposes its motion and is the cause of resistance.

Let's do a check for understanding.

What statement best describes the cause of resistance in a metal wire.

Is it A, the electrons collide with metal ion or B, metal ion move into the way of electrons, or C electrons and metal ions attract.

Pause the video now make a choice and then come back to check your answer.

Welcome back, if you chose electrons collide with metal ions, that's the correct answer.

For answer B, metal ions do not move into the way of electrons, they can't move.

And answer C electrons and metal ions do attract, but the electrons can still drift in between them.

Well done if you got that right.

There are metal ion that cause resistance along the whole length of the wire.

There's metal ion on one, end in the middle, and at the other end.

We can think of each section causing resistance.

Here's a check for understanding.

Which statement best describes resistance in a uniform metal wire.

Is it A, resistance is greatest at the end? B, resistance is greatest in the middle.

Or C resistance is the same along every section of the wire.

Pause a video, make a choice, and then come back to check how you've done.

Welcome back, if you chose answer C, resistance is the same along every section of the wire, that's the correct answer.

The wire contains metal ions along its whole length, and so every section of the wire causes resistance.

It's not greater in the middle or at the ends.

Well done if you got that right.

This length of nichrome wire is like short sections each with a little bit of resistance joined together end to end.

The wire can also be thought of lots of little resistors connected to each other in series.

It's easier to push current through a single resistor than through many resistors connected in series.

Likewise, it's easier to push current through a short length of wire than through many lengths joined end to end together.

So it's easier to push current through a short wire than a long wire.

This means a short wire has a lower resistance than a long one.

There are fewer metal ions to collide with in the shorter wire.

Here's a true/false check for understanding.

The statement is a long wire has lower resistance than a short wire.

Is this true or false? Pause the video now, make your choice and then come back to check how you've done.

Welcome back, if you chose false.

That's correct.

A long wire does not have a lower resistance than a short wire.

Now's the time to justify your answer.

The two justifications are, A, there are more metal ions along the wire or B, that are more electrons along the long wire.

Pause the video now, make your choice and then come back to check how you've done.

Welcome back, if you chose A, there are more metal ions along the long wire, that's correct.

There's more metal ion because there's more wire, so that causes more resistance.

In answer B, there are more electrons along the long wire, but that doesn't affect the resistance.

Well done if you got that right.

In the moving people model, there are only a few seats in the way in a short section like this.

In a longer section, increasing the length increases the number of seats in the way, and so increases the resistance.

Let's try a check for understanding.

Which statement is true about the moving people model? Is it A, a narrow space has more seats or B, a longer space is easier to get through or C, the seats get in the way? Pause the video now and using the image make your choice, then come back to check your answer.

Welcome back, if you chose answer C, that's correct.

The seats get in the way of these people trying to walk through the narrow space.

Answer A, the narrow space has more seats is not correct.

There'll be fewer seats if there's less space for them and B, a longer space is not easy to get through.

If it's longer, it'll be more difficult.

Well done if you got that right.

We've reached the end of this section.

Now's the chance to practise what you've learned.

You're going to test how much current can flow through different lengths of the same wire.

You should start with a length of 100.

0 centimetres and then decrease it by 20.

0 centimetres each time.

Finishing at the 20.

0 centimetre length.

You will use ammeter to measure the current and you'll measure the current through each length three times and then calculate the mean current through each one.

The circuit is shown and also the table for your results is there as well.

Once you've got your results, describe what you found and compare the measurements of current with length.

Pause the video now and come back when you're ready to check how you've done.

Let's look at a sample set of results.

For the length of the wire at 100.

0 centimetres.

The currents were 0.

085, 0.

089 and 0.

089 amps.

This gives a mean of 0.

088.

for the 80.

0 length the currents were 0.

112, 0.

113, 0.

106, which gives a mean of 0.

110.

For the 60.

0 centimetre length, we start with 0.

440 and then we have 0.

144, 0.

148.

It looks like the 0.

440 reading, the first one at 60.

0 centimetres was anomalous, so we're not going to use this one to calculate the mean, so only using the second and third readings we get a mean of 0.

146.

At 40.

0 centimetres, we had 0.

219 0.

223, 0.

219.

That gives a mean of 0.

220.

Lastly, at 20.

0 centimetres we had 0.

435, 0.

431 and 0.

450, which gives a mean of 0.

439.

Describing what we found, as the length decreased, the mean current increased.

This means that the resistance decreases as the length decreases.

Comparing the measurements of current with length, each time the length was reduced, the current increased.

The current at 80.

0 centimetres was 0.

110 amps and at 40.

0 centimetres was 0.

220 amps.

When the length halved, going from 80 to 40 centimetres, the current doubled going from 0.

110 to 0.

220.

The current at 20.

0 centimetres was 0.

439 amps and the current at 40.

0 centimetres was 0.

220 amps.

This means when the length doubled from 20 to 40 centimetres, the current halved, going from 0.

439 to 0.

220.

This isn't exactly half, but it's close enough so we can say the resistance halved when the length halved and the resistance doubled when the length doubled.

You could also say that the resistance and the length are proportional.

Well done if you've got similar results.

We are now ready to look at the resistance of wire of different lengths.

Let's start by examining the results.

So when the length of the wire increases the current decreases, this means the resistance increases.

Doubling the length from 20.

0 centimetres to 40.

0 centimetres caused the current to halve from 0.

439 amps to 0.

220 amps.

0.

220 times two is 0.

440, which is close enough to 0.

439.

If the current is halved, the resistance has doubled.

Doubling the length from 40.

0 centimetres to 80.

0 centimetres causes the current to halve from 0.

220 to 0.

110 amps.

The resistance has doubled again.

Increasing the length by three times from 20.

0 centimetres to 60.

0 centimetres causes the current to decrease from 0.

439 amps to 0.

146 amps.

0.

146 times three equals 0.

438, which is close enough to 0.

439.

The resistance has increased by a factor of three.

When the length and resistance increased by the same factor, we can say that the resistance is proportional to the length.

Let's do a check for understanding.

What would the current be for a length of 50.

0 centimetres long.

Use the table of results alongside to help you calculate this.

Pause the video now, do your calculations and make your choice and then come back to check how you've done.

Welcome back, if you chose 0.

176, you're correct.

The current for 100.

0 centimetre length is 0.

088 amps.

For of 50.

0 centimetre length, the current will be double, so two times 0.

088 equals 0.

176 amps.

Well done if you got that right.

That was quite a tricky question.

In the moving people model, there are three seats in the way in a short section.

Doubling the length doubles the number of seats to six and so doubles the resistance.

Here's a true or false check for understanding.

The statement is, in the moving people model, increasing the length and the number of people will allow a higher current to flow.

Is this true or false? Pause the video now.

Make your choice and then come back to check your answer.

Welcome back, if you chose false.

That's correct.

Let's look at the that you could use.

Justification A is, more people is like more charge or a higher current.

Justification B is, more seats make it harder to move, so the current is reduced.

Pause the video now, choose the correct justification and then come back to see how you've done.

Welcome back, if you chose justification B.

That's correct.

If there's more seats, it's harder for the people to move, so there's less current.

Justification A thinks about the people, but it doesn't take into account that the people will bump into more seats so it isn't the right justification.

Well done if you got that right.

Cutting a long wire in half reduces the number of metal ions to collide with and so reduces the resistance.

If the wire has halved the resistance halves because there's half the number of iron.

Let's check your understanding.

What will happen to the current a thin wire carries if it is cut into three equal lengths and only one length is used.

The choices are A, the current will be three times bigger.

B, the current will stay the same or C, the current will be three times smaller.

Pause the video now, make your choice and then come back to check how you've done.

Welcome back, if you chose answer A, the current will be three times bigger, that's correct.

We've reduced the length, so we've reduced the resistance and so the current will be higher.

It won't stay the same and it won't be smaller.

Well done if you got that right.

Each of these resistors has a resistance of 1 ohm.

The total resistance is one plus one plus one plus one plus one, so five ones equals five ohms. The resistance of two resistors is two ohms and the resistance of three resistors is three ohms. Let's try a check for understanding.

A 10 centimetre wire with the resistance of 10 ohms is cut into a six centimetre and a four centimetre length.

What is the resistance of each piece of wire? The choices are A, the resistance of the six centimetre length is six ohms. The resistance of the four centimetre length is four ohms. Or B, the resistance of the six centimetre length is four ohms and the resistance of the four centimetre length is six ohms or finally C, both lengths have a resistance of five ohms. Pause the video now.

Make your choice and then come back to see how you've done.

Welcome back, if you chose answer A, that's correct.

The resistance of the six centimetre length will be six ohms 'cause each centimetre has a resistance of one ohm and the resistance of the four centimetre length will be four ohms because it's four centimetres each with one ohm resistance.

Well done if you got that right.

We've reached the end of the section.

Let's do a task to practise what you've learned.

100.

0 centimetre length of uniform nichrome wire has a resistance of exactly 200 ohms. Explain how it would be possible to make three resistors of 100 ohms, 50 ohms, and three ohms from this length of wire.

You can use wire cutters and an accurate metre ruler.

Pause the video now, write out your answer and then come back to see how you've done.

Welcome back, so to get 100 ohms, 100 ohms is a half of 200 ohms. So if the wire is cut exactly in half to make a 50.

0 centimetre length, it will have a resistance of 100 ohms. To make a 50 ohm resistor, 50 ohms is half of 100 ohms, so if the remaining 50 centimetre length is cut in half to give exactly 25.

0 centimetres, it'll have a resistance of 50 ohms. To get three ohms from the length of wire, a hundred centimetres gives 200 ohms. 50 centimetres gives 100 ohms, 25 centimetres gives 50 ohms, which means one centimetre would give two ohms. So 1.

5 centimetres will give three ohms. The number of ohms is twice the number of centimetres.

Well done if you completed that task correctly.

That was quite tricky.

We've reached the end of the lesson, so let's summarise what you've learned.

The resistance of a wire is caused by the electrons colliding with metal ions.

A longer wire will have more metal ions causing collisions.

It will have a higher resistance.

Doubling the length of a uniform wire will double the number of metal ion.

It will double the resistance of the wire.

The resistance of a wire is proportional to its length.

You've done really well to complete this lesson.

I hope to see you again soon.