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# Voltage and Length Question! watch

1. Hey guys, so I had a Physics experiment assignment, and the experiment was the following:

Measuring the voltage across a sheet of conductive paper by using a probe and then reading of the voltmeter, from lengths between 2 - 30cm (went up in 2cm intervals). I then drew a graph of voltage against length for my results and got a positive gradient straight line, and for every 2cm interval I had, the voltage would increase by roughly 0.4V each time. I was wondering if lower emf was used, what would happen to the gradient of my graph? Would it decrease or stay the same or what? Many thanks!
2. The gradient will depend on the emf in this case.
If you had an emf of 20V, for example, the voltage would increase from around zero to 20V as you move the contact along the paper.
If the emf was only 2V then you would get a voltage from about 0 to 2V over the same distance.
So a graph of emf against distance would have a smaller gradient.
3. (Original post by Stonebridge)
The gradient will depend on the emf in this case.
If you had an emf of 20V, for example, the voltage would increase from around zero to 20V as you move the contact along the paper.
If the emf was only 2V then you would get a voltage from about 0 to 2V over the same distance.
So a graph of emf against distance would have a smaller gradient.
Hey there The voltage at the start went from -2V and to the end it went to 3V (I forgot the emf of the battery we used though I think it may have been 6V). So your telling me if I had an emf of 20V and used the probe on different distances, there would be a greater change in V than as opposed to if the emf used was 2V, right?
The graph was Voltage against length (the voltage being the reading on the voltmeter at each distance measured).
4. Yes. You didn't give details of the rest of the circuit so I don't know exactly how your sample is connected up to the emf, or the probe to the sample. But in principle, if you increase the emf across the sample, then the probe will measure a bigger voltage difference between one end of it and the other. This means a bigger gradient on a voltage against distance graph.
5. (Original post by Stonebridge)
Yes. You didn't give details of the rest of the circuit so I don't know exactly how your sample is connected up to the emf, or the probe to the sample. But in principle, if you increase the emf across the sample, then the probe will measure a bigger voltage difference between one end of it and the other. This means a bigger gradient on a voltage against distance graph.
The battery pack was connected to 2 clip holders and the probe was just pressed against the paper. The second part of the investigation is a bit weird; we had to do this second experiment with the same procedure, except the paper was thicker in one side than the other, so when I drew my graph I got 2 lines of best fit, of which the thicker side had a smaller gradient than the thinner side, and the question says that 1 student took measurements around the change in gradient whereas another student took measurements of both lines, and it asks which student's method was better and why, any thoughts?
6. The answer to which method is "best" depends on what the actual aim of the experiment is.
How effective the experiment is can only be judged against the required outcome.

If the paper has two different thicknesses, then it has two different resistance per unit length values.
The thinner paper will have a higher resistance per unit length.
This means that the pd across the thinner paper section will be greater than that across the thicker section.
(For the same length of the two sections)
The current is the same through both halves so as V=IR the higher voltage will be across the thinner paper.
This should result in the voltage changing more quickly with distance across the thinner paper.
The graph would (should) consist of two straight lines with different gradients. The larger gradient being the one for the thinner paper.
The gradient is a measure of resistance per unit length of paper.
I don't see any point in measuring near the change in gradient unless the question specifically asks about what happens there. It seems more likely that you would be interested in measuring the differences between the two halves of the paper, and therefore the values of the two gradients.
7. (Original post by Stonebridge)
The answer to which method is "best" depends on what the actual aim of the experiment is.
How effective the experiment is can only be judged against the required outcome.

If the paper has two different thicknesses, then it has two different resistance per unit length values.
The thinner paper will have a higher resistance per unit length.
This means that the pd across the thinner paper section will be greater than that across the thicker section.
(For the same length of the two sections)
The current is the same through both halves so as V=IR the higher voltage will be across the thinner paper.
This should result in the voltage changing more quickly with distance across the thinner paper.
The graph would (should) consist of two straight lines with different gradients. The larger gradient being the one for the thinner paper.
The gradient is a measure of resistance per unit length of paper.
I don't see any point in measuring near the change in gradient unless the question specifically asks about what happens there. It seems more likely that you would be interested in measuring the differences between the two halves of the paper, and therefore the values of the two gradients.
The aim of the experiment was to see how the voltage varied with the probe placed in different lengths, thickness was not specified in the experiment but was just something I noticed during it. And yes that's absolutely correct, the larger gradient was with the thinner paper. The question said 1 student wanted to take more readings around the change in gradient on the graph but another wanted to take more readings on the 2 straight lines so they were accurate, surely the first one would be right so that he can identify if the change in gradient was an anomolous result or not right?
8. Again, it depends what you want to find out.
If you want to get accurate results for gradient, you take more measurements on the linear parts.
For example, if you want to find out where the transition takes place between thinner and thicker paper, it would be indicated by the place the two lines intercept. This is determined more accurately by making sure your two straight lines are as accurate as possible.

The place where the change occurs could be abrupt or could be gradual.
If you wanted to look at that, you would need to take a lot of measurements close together near the change. This is done assuming that there is a change.

If you believe that there should not be a change in gradient, then you need to measure the gradient more accurately by getting more accurate data points all along the line.

As I say, what you do is determined by what you want to know.
9. (Original post by Stonebridge)
Again, it depends what you want to find out.
If you want to get accurate results for gradient, you take more measurements on the linear parts.
For example, if you want to find out where the transition takes place between thinner and thicker paper, it would be indicated by the place the two lines intercept. This is determined more accurately by making sure your two straight lines are as accurate as possible.

The place where the change occurs could be abrupt or could be gradual.
If you wanted to look at that, you would need to take a lot of measurements close together near the change. This is done assuming that there is a change.

If you believe that there should not be a change in gradient, then you need to measure the gradient more accurately by getting more accurate data points all along the line.

As I say, what you do is determined by what you want to know.
Alright I understand, by the way how would you reduce uncertainty in this experiment?
10. If the aim of the measurements is to find the gradient of the line (or both lines with different gradients) then the simplest, and standard, method is to take as many points as possible. The more you take, the lower the probable error.
The actual uncertainty in the gradient will become apparent when you try to plot the points and see how they fall (or don't!) on a straight line. More data points will allow you to see if there are any measurements that look like they need to be repeated, for example, because they fall a long way from the best fit line.
11. (Original post by Stonebridge)
If the aim of the measurements is to find the gradient of the line (or both lines with different gradients) then the simplest, and standard, method is to take as many points as possible. The more you take, the lower the probable error.
The actual uncertainty in the gradient will become apparent when you try to plot the points and see how they fall (or don't!) on a straight line. More data points will allow you to see if there are any measurements that look like they need to be repeated, for example, because they fall a long way from the best fit line.
If the aim of the experiment is to see how length affects voltage, is taking as many points as possible the only way to reduce probable error in this case?
12. (Original post by Nator)
If the aim of the experiment is to see how length affects voltage, is taking as many points as possible the only way to reduce probable error in this case?
If you look at the individual measurements you take, we have voltage and length.
Voltage
I take it you are using a standard multimeter. There is not much you can do to reduce the uncertainty/error here. The meter will have its own "accuracy" rating, usually given by the manufacturer. (This is not the same as the precision of the meter, which is the smallest change the scale can register).
The meter's accuracy is usually given as a percentage and can often be found on the back or in the user guide. There is nothing much you can do about this, though! The best I can suggest is really just common sense.
If you are measuring 1 volt then you would make sure you are on the lowest suitable range, eg the 0 to 1.5V range rather than the 0 to 9V range.
Length
I'm not sure how you have actually done this bit. Is the paper marked at measured intervals? How, exactly, have you decided where the 2cm intervals are?
How closely can you place the meter probe on the mark on the paper.
You should, I suppose, be careful about how hard you press the probe onto the paper. Not hard enough and you have a bad contact; too hard and you crush the paper, changing its resistance slightly. If this was happening, you would see the measured value change while you were doing it and moving the probe about.
I can't see any obvious way to reduce the errors here. The taking of repeated measurements is the standard procedure.
The aim "to see how something behaves" is rather vague. It doesn't actually specify that you are trying to calculate any particular value or have any hypothesis.
As a result, when you have your results, a graph, what do you do next?
Errors and uncertainties relate the measurements you take to the confidence you have in your final calculation or conclusion.
So once you have a final value or hypothesis, then you can meaningfully talk about how likely you are to be near the truth.
If your hypothesis/conclusion is that the resistance (voltage) varies uniformly with length, then it's the quality of the data and the straight line that matters.
If you conclude that there are two different "thicknesses", then the quality of the two lines and the certainty that there are actually two different slopes, and not one with highly erratic points, will hopefully confirm this.
13. (Original post by Stonebridge)
If you look at the individual measurements you take, we have voltage and length.
Voltage
I take it you are using a standard multimeter. There is not much you can do to reduce the uncertainty/error here. The meter will have its own "accuracy" rating, usually given by the manufacturer. (This is not the same as the precision of the meter, which is the smallest change the scale can register).
The meter's accuracy is usually given as a percentage and can often be found on the back or in the user guide. There is nothing much you can do about this, though! The best I can suggest is really just common sense.
If you are measuring 1 volt then you would make sure you are on the lowest suitable range, eg the 0 to 1.5V range rather than the 0 to 9V range.
Length
I'm not sure how you have actually done this bit. Is the paper marked at measured intervals? How, exactly, have you decided where the 2cm intervals are?
How closely can you place the meter probe on the mark on the paper.
You should, I suppose, be careful about how hard you press the probe onto the paper. Not hard enough and you have a bad contact; too hard and you crush the paper, changing its resistance slightly. If this was happening, you would see the measured value change while you were doing it and moving the probe about.
I can't see any obvious way to reduce the errors here. The taking of repeated measurements is the standard procedure.
The aim "to see how something behaves" is rather vague. It doesn't actually specify that you are trying to calculate any particular value or have any hypothesis.
As a result, when you have your results, a graph, what do you do next?
Errors and uncertainties relate the measurements you take to the confidence you have in your final calculation or conclusion.
So once you have a final value or hypothesis, then you can meaningfully talk about how likely you are to be near the truth.
If your hypothesis/conclusion is that the resistance (voltage) varies uniformly with length, then it's the quality of the data and the straight line that matters.
If you conclude that there are two different "thicknesses", then the quality of the two lines and the certainty that there are actually two different slopes, and not one with highly erratic points, will hopefully confirm this.
Yes it is a standard multimeter and right As for length, I had to measure 2cm intervals myself, and then mark them with a pencil at each interval. And that is good help, never thought that pressing the probe lighter/harder may alter the reading on the voltmeter, thanks for that information
14. Also: can you identify a random error in this experiment and anything which can be done to reduce the risk of random error? And any systematic errors present here?
15. The measurements I was talking about in post 12 are what are called random errors. These are the errors made simply by doing the measurement. In your case, marking and measuring the 2cm lengths on the paper will be a source of random error.
Systematic errors are those you don't usually know about, such as errors in the meter where, possibly, it hasn't been "zeroed" correctly. (It doesn't read zero when there is no current, for example.)
You only really find out about these when you look at the results and see that something is clearly wrong.
I would have no way of knowing what these are in your experiment. (If there are any)
16. (Original post by Stonebridge)
The measurements I was talking about in post 12 are what are called random errors. These are the errors made simply by doing the measurement. In your case, marking and measuring the 2cm lengths on the paper will be a source of random error.
Systematic errors are those you don't usually know about, such as errors in the meter where, possibly, it hasn't been "zeroed" correctly. (It doesn't read zero when there is no current, for example.)
You only really find out about these when you look at the results and see that something is clearly wrong.
I would have no way of knowing what these are in your experiment. (If there are any)
So the pressing of the probe and marking of the intervals would be random errors? And alright then fair enough Also, going back to the lower emf and gradient question, originally 0V was reached at 14 cm, so if lower emf was used, what would happen to the place where 0V is reached? It would be greater or less than 14cm?
17. Marking and measuring the intervals will introduce random error. Yes.
The pressing of the probe is more tricky. If you assume that the amount of pressure you use each time is random, then yes.

I'm not sure what the significance of 0V is without seeing a circuit diagram, showing how you have connected the supply to the resistance paper, and the meter to this.
If you are trying to find the point where the thickness changes then it's where the two straight lines cross on the graph. As you are measuring changes in voltage along the paper, it's not really the actual value of the voltage at any point that matters, but the change in voltage from one point to the next.
For example, if you measured -0.8V, -0.5V, -0.2V, +0.1V, +0.4V along the paper at equal intervals, it would have exactly the same significance (a straight line) as +0.3V, +0.6V, +0.9V, +1.2V etc.

The zero volt level in a circuit is usually "earth potential" and has no significance other than that it is an arbitrary reference voltage. I'm not sure why this should be in the middle of the paper somewhere. As I say, without the circuit details I really can't say.
18. (Original post by Stonebridge)
Marking and measuring the intervals will introduce random error. Yes.
The pressing of the probe is more tricky. If you assume that the amount of pressure you use each time is random, then yes.

I'm not sure what the significance of 0V is without seeing a circuit diagram, showing how you have connected the supply to the resistance paper, and the meter to this.
If you are trying to find the point where the thickness changes then it's where the two straight lines cross on the graph. As you are measuring changes in voltage along the paper, it's not really the actual value of the voltage at any point that matters, but the change in voltage from one point to the next.
For example, if you measured -0.8V, -0.5V, -0.2V, +0.1V, +0.4V along the paper at equal intervals, it would have exactly the same significance (a straight line) as +0.3V, +0.6V, +0.9V, +1.2V etc.

The zero volt level in a circuit is usually "earth potential" and has no significance other than that it is an arbitrary reference voltage. I'm not sure why this should be in the middle of the paper somewhere. As I say, without the circuit details I really can't say.
Just the point at which V = 0, would a lower emf affect this position (of 14cm in this case)? And The circuit read negative up to this point, and positive after this point. The circuit was all set up for us, and it just had a battery pack, and 2 clip holders connect to the rest of the wires. Any thoughts what would happen to the place of 0V? Would it remain the same?
19. It's impossible to be sure. It depends how the circuit was set up and why there is a zero volt point in the middle somewhere.
If the one end of the paper was held at, say, -6V and the other at +6V, (=12V)then increasing the emf could (and I repeat could) change it to -9V to +9V, for example, giving 18V. On the other hand, it could change to -3V to +15V (also giving 18V).
The zero point will be different in each case.
As a general rule, the position where the voltage is zero will change if you change the pd across across the whole paper if the paper has two different thicknesses.
If it has constant thickness, the zero position could stay in the same place.
Sorry I can't be more precise.
20. (Original post by Stonebridge)
It's impossible to be sure. It depends how the circuit was set up and why there is a zero volt point in the middle somewhere.
If the one end of the paper was held at, say, -6V and the other at +6V, (=12V)then increasing the emf could (and I repeat could) change it to -9V to +9V, for example, giving 18V. On the other hand, it could change to -3V to +15V (also giving 18V).
The zero point will be different in each case.
As a general rule, the position where the voltage is zero will change if you change the pd across across the whole paper if the paper has two different thicknesses.
If it has constant thickness, the zero position could stay in the same place.
Sorry I can't be more precise.
I see what you mean, and is it possible to deduce if the position where the voltage is zero would decrease/increase with lower/greater emf?

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