# A question about uncertainty using a regression line and experimental data

• DanDavies
In summary, the conversation was about a student seeking assistance with understanding uncertainty in an experiment involving a simple circuit with a dry cell and variable resistor. They used an ammeter and voltmeter to take measurements and then plotted a VI graph to calculate EMF and internal resistance. They also mentioned the digital minimum displays for the instruments. The student asked for help in calculating the uncertainty for r and ξ using a linear regression equation.
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)) %?

Last edited by a moderator:

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.

## What is a regression line and how is it used in scientific research?

A regression line is a statistical tool used to analyze the relationship between two variables. It is used in scientific research to determine the strength and direction of the relationship between a dependent variable and one or more independent variables.

## How does uncertainty affect the validity of experimental data?

Uncertainty refers to the degree of error or variability in the data. It can affect the validity of experimental data by introducing bias or making it difficult to draw accurate conclusions. High uncertainty may indicate that the results are not reliable and more research is needed to confirm the findings.

## What are some common sources of uncertainty in experimental data?

Some common sources of uncertainty in experimental data include measurement error, sampling bias, human error, and environmental factors. These sources can introduce variability and affect the accuracy of the data collected during an experiment.

## How can a regression line help to account for uncertainty in experimental data?

A regression line can help to account for uncertainty by providing a visual representation of the relationship between variables, including any patterns or trends. It can also be used to calculate the margin of error and determine the level of confidence in the results.

## What are some limitations of using a regression line to analyze experimental data?

One limitation of using a regression line is that it assumes a linear relationship between variables, which may not always be the case. Additionally, it may not account for all sources of uncertainty in the data, and the results may be influenced by outliers or influential data points. It is important to consider these limitations when interpreting the results of a regression analysis.

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