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!

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 27032011 00:26

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 27032011 09:32
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. 
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 27032011 12:20
(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.
The graph was Voltage against length (the voltage being the reading on the voltmeter at each distance measured). 
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 27032011 12:50
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.

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 27032011 13:11
(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. 
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 27032011 15:27
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. 
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 27032011 17:03
(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. 
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 27032011 17:22
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. 
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 28032011 12:36
(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. 
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 28032011 13:47
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. 
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 28032011 15:12
(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. 
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 28032011 17:55
(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?
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. 
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 28032011 18:33
(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. 
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 28032011 19:49
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?

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 28032011 20:00
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) 
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 28032011 20:34
(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) 
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 28032011 21:27
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. 
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 28032011 21:46
(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. 
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 28032011 22:11
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. 
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 28032011 22:19
(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.
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