A question about uncertainty using a regression line and experimental data

[DanDavies]

Homework Statement

I'm new to uncertainty, so I needed a little assistance. The circuit in this experiment was simple, a dry cell connected to a variable resistor. I used an ammeter on the circuit and used a voltmeter across the resistor and took some measurments.

The experiment was to calculate EMF and Internal resistance using the results we obtained by plotting a VI graph.

The ammeter and voltmeter were digital, their minimum display were 0.01V & 0.01A

Can anyone explain to me how to get the uncertainty for r and for ξ?

Homework Equations

http://img686.imageshack.us/img686/1408/29533548.jpg

If the image doesn't work: http://img686.imageshack.us/img686/1408/29533548.th.jpg

The Attempt at a Solution

100(0.01/(5.83-0.45))+(0.01/(1.35-0.10)) %?

 

[ideasrule]

For calculating uncertainty, you can use this equation:

http://en.wikipedia.org/wiki/Regression_analysis#Linear_regression

 

[kerimek]

I understand your confusion about uncertainty and how to calculate it in this experiment. Uncertainty is an important aspect of any scientific measurement and it is important to consider it when analyzing data.

In this case, uncertainty can be calculated using the regression line that you have plotted. The regression line is a mathematical representation of the relationship between the voltage and current in your circuit. It can be used to determine the uncertainty in both the internal resistance (r) and EMF (ξ).

To calculate the uncertainty in r, you can use the formula:

uncertainty in r = slope of regression line x uncertainty in voltage / average current

Similarly, to calculate the uncertainty in ξ, you can use the formula:

uncertainty in ξ = y-intercept of regression line x uncertainty in current / average current

In these formulas, the uncertainty in voltage and current can be determined from the minimum display values of your digital ammeter and voltmeter.

It is also important to note that uncertainties can be propagated through calculations, so if you are using the calculated values of r and ξ to determine other quantities, the uncertainty will also need to be taken into account in those calculations.

I hope this helps clarify the process of determining uncertainty in this experiment. If you have any further questions, please don't hesitate to ask.