Hello, my name's Dr.

George, and this lesson is called Resistance of a Wire at a Constant Temperature, and it's part of the unit Electric Fields and Circuit Calculations.

The outcome for the lesson is I can describe how to investigate the resistance of a wire at a constant temperature and make scientific conclusions.

Here are the key words for the lesson.

I'll remind you what they mean as we go along, but you can come back to this slide anytime if you want to check the meanings for yourself.

The lesson has two parts, measuring the resistance of a wire, and explaining how resistance changes.

Let's take a look at the first part.

The resistance of a piece of wire depends on these factors.

The length of the wire, that would be the length when it's straight, the cross-sectional area of the wire, how much area the end has, the type of metal the wire is made from, and the temperature of the wire.

So let's see how many of those you can remember.

Which of the following are variables that can affect the resistance of a metal wire? And with short questions like these, I'll wait five seconds, but if you need longer, just press pause and press play when you're ready.

So the answers are, the length of the wire, the temperature of the wire and the diameter of the wire.

These affect the resistance.

Now we're going to investigate how the length of a wire affects its resistance exactly.

Now in this, the length is the independent variable and the resistance is the dependent variable.

So the independent variable is the one that the experimenter deliberately changes, sets different values of it, and the dependent variable is the one that the experimenter measures to see how it's affected by the changing independent variable.

And to do this, you can use a circuit, like the one here.

So the current is measured with an ammeter, the potential difference or voltage is measured with a voltmeter.

So we have here just a simple series circuit with only a cell and the piece of wire we're testing in it, but the ammeter has been added in series and the voltmeter in parallel with a piece of wire.

And we can vary the length of the wire in the circuit by moving a crocodile clip along the wire.

And we can then calculate the resistance of the wire using resistance as voltage potential difference divided by current.

And of course, that metre ruler is not part of the circuit, but it's there so we can measure the length of the wire.

Now, which of following is the correct equation for calculating resistance? Press pause if you need longer than five seconds and press play when you're ready.

And the correct equation is resistance is voltage divided by current.

Remember, resistance is a measure of how difficult it is for current to flow through something.

If you had a large voltage, which is like giving a large push to the electrons, but you still only got a small current, then you do large number divided by small number here, and that will give you a large number, a large resistance for the result.

Now to change the independent variable, the length of the wire, you move the crocodile clip, and in this experiment, you'd move it by about 10 centimetres each time.

It doesn't have to be an exact round number as long as your values of the independent variable are well spread out across the range of values that you're using, then you can read the value from the ruler to the nearest millimetre, to the nearest 0.

1 centimetres.

You want to try to keep the wire as straight as possible.

If it's not straight, then you're not really measuring its length.

Also, take the reading with your eye directly over the crocodile clip, directly above it.

If you read at an angle from one side or the other, you will get a measurement error, the crocodile clip will look like it's next to a different marking on the ruler from what it's really next to.

Now, what's the precision or smallest interval that a ruler with millimetre divisions can measure to? Is it 0.

1 metres, 0.

01, 0.

001 or 0.

0001? Press pause if you need more time to think.

And if the ruler has millimetre divisions, you can measure to the nearest millimetre, which is a thousandth of a metre or 0.

001 metres.

Now since the measurements of current, potential difference, and length are quite quick and easy to take, you'll be able to take quite a lot of different readings, the different values.

And so, you can do that instead of taking repeat readings for the same length.

Because to avoid random errors, you want to be able to see clearly where to draw your best fit line on a graph, and you can either do that by having values where you've repeated and averaged to make the individual values more accurate, or you can do that by having lots of points on your graph.

Now to make this a fair test, we have to think about keeping some variables the same.

So we're going to keep the following control variables the same, the material of the wire, you're not going to suddenly change that partway through the investigation, the cross-sectional area of the wire.

And as far as you can, the temperature of the wire.

And that's because any of these variables will affect the resistance, and you are trying to see how the length affects the resistance.

If you change something else as well, then you won't be able to be sure whether the resistance is being affected just by the length or also by other changing variables.

So if you use the same piece of wire, and if it's uniform, it has the same cross-sectional area along it, then the material and the cross-sectional area will naturally be constant.

The temperature can increase because of the current, and this can be controlled reasonably well by switching the current on just while you're making a reading and then immediately switching off between readings.

And that allows the wire to cool back to room temperature each time so that each time you take a measurement, the wire has the same temperature.

So which of the following are control variables in the investigation of how length affects the resistance of a wire? Press pause if you need longer than five seconds to think.

And the correct answer is the diameter of the wire and the type of wire.

The length is your independent variable, you're going to deliberately change that, you can't keep it the same, and the colour doesn't matter.

So now you're going to do the investigation.

You'll set up the circuit shown to measure the length and find the resistance of a piece of wire made of material called nichrome.

Then you'll record your results in a table like the one shown, and notice that there's a column on the right for resistance, you can calculate those resistances and add them to the table.

Take measurements at the lengths of 100 centimetres down to about 30 centimetres in steps of roughly 10 centimetres, and then plot a graph of resistance against length.

That's resistance on the Y axis, and length, the independent variable, on the X axis.

So while you're doing the task, press pause, and press play when you've collected your results, I hope your experiment went well.

Here's a set of example results, and if for any reason you weren't able to get a set of results, you could use these to plot a graph And I'll show you what that graph would look like.

So here's a graph of those results.

There's a best fit line drawn, and we noticed that the resistance at about 40 centimetres seems like an anomalous point, it doesn't fit the general pattern, the other points are all very close to this one straight line.

So we would ignore that when we draw the line of best fit.

And the line of best fit is a straight line that passes through the origin, it passes through 0-0.

We wouldn't have been able to actually take a measurement at 0-0, you see, there isn't a cross there because we can't do this experiment with zero length of wire.

But it should be reasonably clear that if the length of the wire could be zero, then it would have zero resistance.

Now let's look at explaining how resistance changes.

So first of all, going back to that best fit line, it's straight, it passes through the origin.

And when we see that on a graph, we have a particular kind of relationship between the two variables.

They're directly proportional, so the resistance is directly proportional to the length.

The anomalous point could have been caused by some kind of measurement error or the wire heating up.

Now, which of these three graphs shows a directly proportional relationship? Now the only one of these graphs that shows direct proportion is B.

It's not enough for the graph to be straight, as in A, it's not enough for the graph to be straight and have a positive gradient, as in C.

It needs to pass through the origin.

And in this kind of relationship, when one variable is multiplied by a number, the other variable is multiplied by the same number.

So for example, if the length of the wire doubles, its resistance doubles.

Now another way to keep the temperature constant, apart from not keeping the current on for too long and letting the wire cool down, is to place the wire in a water bath.

But you can't fit a one metre length of wire straight into a beaker.

So you coil it around a piece of wooden dowel, just a cylinder of wood.

But it is important you keep the water at constant temperature.

Coiling up the wire doesn't affect its resistance.

But the coil has to be removed, shortened, and measured each time a reading is made.

So in this version of the experiment, it's not as straightforward to change the length of the wire.

And the wire needs to be wound so that it doesn't overlap with itself because that would shorten the conducting length.

If it overlapped with itself, then current would be able to go straight across without going around each turn of the coil.

And the water has to be stirred and replaced after each reading to keep the temperature the same.

The wire will heat up a little bit when current passes through it, and that will heat the water up a little bit so you can then replace the water with new water that's at room temperature.

And the coils should be in the middle of the beaker so that water can easily circulate around it.

Otherwise you can get hotspots, areas of water that are warmer than other parts of the water, and then you might not get a temperature reading that actually reflects the true temperature where the coil is.

So which of the following would not help keep the temperature of the coil of wire constant? Have a look at those, press pause while you're thinking and press play when you're ready.

The correct answer is the dowel should be an electrical conductor.

Well, that's not something you want because it means current can pass straight through the dowel instead of going around the turns of the coil and it wouldn't do anything to help keep the temperature constant.

We've seen that the resistance of a wire is directly proportional to its length.

We have this straight line passing through the origin on the graph.

So if the length increases by a factor, the resistance increases by the same factor.

A question about that, a 10.

0 centimetre length of uniform nichrome wire has a resistance of 2.

0 ohms. What resistance will a 2.

0 centimetres length of the same wire have? 0.

1 ohms, 0.

2, 0.

4 or 1.

Press pause while you're thinking and press play when you've chosen your answer.

The correct answer is 0.

4 ohms, and you can look at it this way.

If 10 centimetres has a resistance of two ohms, then one centimetre will have a resistance of 0.

2 ohms, it's a 10th as long, it will have a 10th of the resistance, and then we could double that to two centimetres and then the resistance doubles to 0.

4 ohms. So well done if you got that.

Trying to understand how length affects resistance, we can use what might be called the moving people model.

And we're thinking about resistance in a metal wire and the people are like electrons moving through the wire.

Some of the electrons in a metal are free to move around, they're not bound to individual atoms. And so, these people are walking down a corridor and there are some seats here and they're getting in the way, and these are like the metal ions in the wire.

An ion is an atom that has lost one or more of its electrons, those are the electrons that are free to move around.

And when the seats are in the way of the people, they cause a resistance to the flow of people.

If we double the length of this corridor that the people need to get through, we double the number of seats that are causing resistance.

And so, the resistance due to the seats which represent metal ions is directly proportional to the length, double the length, double the resistance, triple the length, triple the resistance.

And this model can also help explain the heating effects of current 'cause when current flows in a wire, the wire gets warmer.

Well, these people trying to get through the corridor will bump into seats sometimes, and that will make the seats move.

In a real wire, the electrons bump into metal ions making them move more.

And when that happens, there's an increase in temperature.

And that's why current flow causes heating.

Because the movement of the electrons makes the ions move more, they vibrate more.

And if these seats are moving, it's more difficult for the people to get past them.

Current flow causes metal ions to move more, and the moving metal ions then cause the resistance to increase.

It's harder for the electrons to flow through.

Which of the following statements explains why current inner metal wire causes heating? Read the four options.

Press pause while you're thinking and press play when you've decided.

The only statement here that explains why current in a metal wire causes heating is C, current causes the metal ions to move more.

And if a solid's atoms or ions are moving more, vibrating more energetically, that means that that solid has a higher temperature.

The current doesn't cause any change in size of the ions or the electrons.

And the heating isn't caused by the electrons moving more, the current is a flow of charge caused by the flowing electrons, but the heating is caused by energy being transferred to the ions.

And now you're going to write a plan for a slightly different investigation, this time, investigating how resistance varies with the diameter of the wire.

And you'll explain as well how you're going to make it a fair test.

You're going to use nichrome wire again, and wires come in different SWG ratings, that stands for standard wire gauge, and these are different thicknesses.

So imagine you're going to use ratings from this table, they're between 30 and 40, and you can see the diameter for each of those SWG values.

So when you write your plan, you could write it in numbered steps or bullet points, and imagine you are writing it as if you write a recipe.

You want it to be very clear to someone else exactly what to do.

They need to know what order to do things and how to do things, you don't want to leave out important things, like, should I whisk the eggs? Or should I add the flour before or after the butter? So someone else following your plan should be able to get this investigation right.

So while you're writing your plan, press pause, press play when you're finished and I'll show you the key points that you should have included.

I'll show you the points that would be included in a good plan for this investigation.

Take at least five uniform nichrome wires with different SWG ratings, different diameters, between 30 and 40.

Look up the diameters of the wires and note them down.

Measure 100.

0 centimetres of each wire, 'cause you can measure to the nearest millimetre, and measure the current and voltage using the circuit shown.

It's good to include a diagram of the circuit in your plan.

Avoid the wire overheating by switching the current off quickly after taking each reading.

Allow enough time between readings for the wires to cool down to room temperature.

Write the results in a table that has headings for diameter in millimetres, voltage in volts, current, amps, and resistance, ohms, and you should put the units in the headings of your table.

Since only five sets of readings are taken, two repeat sets of measurements should be carried out and a mean calculated for each value of resistance.

Plot a graph of resistance against diameter for the wires tested.

And to explain how you'll make it a fair test, you could say, "This will be a fair test if the wires are all made of nichrome, they all have the same length, 100 centimetres, and they're at room temperature." So well done if you included all of those points or if you included a lot of them, and have a look at any that you missed.

And now we've reached the end of the lesson.

So here's a summary.

The resistance of a metal wire depends on the type of metal, length of the wire, cross-sectional area of the wire and temperature of the wire.

A longer wire will have a higher resistance and the resistance is directly proportional to the length.

When current flows in a metal wire, it will cause the wire to heat up as the electrons collide with metal ions.

This heating also causes the resistance of the wire to increase.

So well done for working through this lesson.

I hope your investigation went well and I hope to see you again in a future lesson.

Bye for now.