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I have no idea how to calculate uncertainties from my boltzmann experiemnt

I have done a boltzmann experiment wherein the voltage across a semiconductor diode was measured and plotted against the log of the current (find throught the resistance- I=V/R).

I'm meant to find the boltzmann constant from the gradient (e/KT) but I have no idea how to calculate the uncertainty of it.

How do I factor in the uncertainty of resistor and the uncertainty of the temperature into my equations.

How also do I understand the error propagation formula here?
Original post by mathsandphysic
I have done a boltzmann experiment wherein the voltage across a semiconductor diode was measured and plotted against the log of the current (find throught the resistance- I=V/R).

I'm meant to find the boltzmann constant from the gradient (e/KT) but I have no idea how to calculate the uncertainty of it.

How do I factor in the uncertainty of resistor and the uncertainty of the temperature into my equations.

How also do I understand the error propagation formula here?


From the uncertainties in the voltage and current measurements, draw error bars on the data points in the graph.

On that graph draw a line which represents the 'best' fit to the data points.
Take that as your probable value for gradient and find the Boltzmann constant.
Then draw a second line which could reasonably pass through the data points and passes through the error bars.
Find the Boltzmann constant from this second line.
Take this as the upper or lower limit in the final result. (Depends where you drew the line)
Use this upper/lower limit to express the plus/minus in the final result.
Exp-slope_uncert.png
Something along these lines. In the example here, an upper AND a lower limit was found.
This is also a possible way of doing this.
Depending on the level at which you are analysing errors, there are alternative methods, but this is pretty standard practice at A-Level
Original post by Stonebridge
From the uncertainties in the voltage and current measurements, draw error bars on the data points in the graph.

On that graph draw a line which represents the 'best' fit to the data points.
Take that as your probable value for gradient and find the Boltzmann constant.
Then draw a second line which could reasonably pass through the data points and passes through the error bars.
Find the Boltzmann constant from this second line.
Take this as the upper or lower limit in the final result. (Depends where you drew the line)
Use this upper/lower limit to express the plus/minus in the final result.
Exp-slope_uncert.png
Something along these lines. In the example here, an upper AND a lower limit was found.
This is also a possible way of doing this.
Depending on the level at which you are analysing errors, there are alternative methods, but this is pretty standard practice at A-Level

Hi, Thanks for the response!! I have done my plots on excel and I'm not sure how to go about calculating uncertainties through that. I am an undergrad year 1 student.
Original post by mathsandphysic
Hi, Thanks for the response!! I have done my plots on excel and I'm not sure how to go about calculating uncertainties through that. I am an undergrad year 1 student.

It's a while since I did one of these, but first here is a link that explains how to add error bars.
Firstly: Draw the graph with the error bars
https://support.microsoft.com/en-us/topic/add-change-or-remove-error-bars-in-a-chart-e6d12c87-8533-4cd6-a3f5-864049a145f0
Then:
I can't find a simple way to do what I have shown in the previous post automatically - if I were doing this now I would print out the graph from Excel and draw the 'worst' fit line by hand and measure it myself.
I haven't tied it, but is it possible to manually move the straight line that excel draws by dragging it with the mouse? This might also be a solution if Excel gives you the gradient of this new line.
Original post by Stonebridge
It's a while since I did one of these, but first here is a link that explains how to add error bars.
Firstly: Draw the graph with the error bars
https://support.microsoft.com/en-us/topic/add-change-or-remove-error-bars-in-a-chart-e6d12c87-8533-4cd6-a3f5-864049a145f0
Then:
I can't find a simple way to do what I have shown in the previous post automatically - if I were doing this now I would print out the graph from Excel and draw the 'worst' fit line by hand and measure it myself.
I haven't tied it, but is it possible to manually move the straight line that excel draws by dragging it with the mouse? This might also be a solution if Excel gives you the gradient of this new line.

If I were to plot the extreme possible values calculated from the minimum and maximum uncertainty and then plotted the gradient of them would that give me the same solution?
Original post by mathsandphysic
If I were to plot the extreme possible values calculated from the minimum and maximum uncertainty and then plotted the gradient of them would that give me the same solution?

I don't think so. But it depends which values you choose.

The point being that you need a best gradient and a 'worst' gradient. Taking, for example, all the highest possible values from the error bars, you would just get a line with almost the same gradient, but just shifted upwards or downwards a bit.

It's one of those things that, for me, works best using my own judgement and eye.
Original post by mathsandphysic
If I were to plot the extreme possible values calculated from the minimum and maximum uncertainty and then plotted the gradient of them would that give me the same solution?

It may be better if you show a picture of what you have plotted and let us know the possible equation(s) that you are using.
Original post by Stonebridge
It's a while since I did one of these, but first here is a link that explains how to add error bars.
Firstly: Draw the graph with the error bars
https://support.microsoft.com/en-us/topic/add-change-or-remove-error-bars-in-a-chart-e6d12c87-8533-4cd6-a3f5-864049a145f0
Then:
I can't find a simple way to do what I have shown in the previous post automatically - if I were doing this now I would print out the graph from Excel and draw the 'worst' fit line by hand and measure it myself.
I haven't tied it, but is it possible to manually move the straight line that excel draws by dragging it with the mouse? This might also be a solution if Excel gives you the gradient of this new line.


Original post by mathsandphysic
If I were to plot the extreme possible values calculated from the minimum and maximum uncertainty and then plotted the gradient of them would that give me the same solution?

Brute force method
https://www.youtube.com/watch?v=U8L3sdWQhmA

A built-in function method
https://www.youtube.com/watch?v=Y-rfyeutais


Hope the 2 videos can solve your issue.

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