Fitting Power Function to Graph Potential vs Distance: What is n?

In summary: The slope of the trendline would indicate the value of k. It might be close, but it's not guaranteed.
  • #1
dapavelko
4
0
I am graphing Potential(Volts) y-axis vs distance (r) x axis. I am asked to fit a power function F(r)=Ar^n . Any ideas on how to do this? What is n supposed to represent?
 
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  • #2


Hi dapaveko, welcome to PF!

EDIT: 'n' is just some number (any number).

'n' is the power (the exponent). 'n' could be 1, or 2, or 3, or 4, or...

in which case the function would be linear, or quadratic, or cubic, or quartic, or ...

The point is that it's some sort of power law. What you get as a result for 'n' depends upon what exponent produces a curve that best fits your data. (I am assuming that you are trying to fit a power law function to some data. Otherwise your question doesn't make much sense).
 
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  • #3


r V
1 8.7
2 4.5
3 2.9
4 2.2
5 1.8
6 1.5

that is my data I got, and I made an excel. I added a trendline curved and got y=8.7715x^-2.011. The data was curved not linear? I am trying to associate the power function F(r)=Ar^n and determine n. Wouldn't n be the -2.011? Sorry your answer confused me so I added the data.
 
  • #4


dapavelko said:
r V
1 8.7
2 4.5
3 2.9
4 2.2
5 1.8
6 1.5

that is my data I got, and I made an excel. I added a trendline curved and got y=8.7715x^-2.011.

Okay.

dapavelko said:
The data was curved not linear?

Are you asking me or telling me? Obviously if n is anything other than 1, then the data will not be linear. What were you expecting it to be like? Are the data curved? Does your fit look like a good fit?

dapavelko said:
I am trying to associate the power function F(r)=Ar^n and determine n. Wouldn't n be the -2.011?

Yes, of course. Excel has determined that n = -2.011 for you.

By the way, I edited my first post slightly.

dapavelko said:
Sorry your answer confused me so I added the data.

What, specifically, about it confused you?
 
  • #5


ok I reread your post and I thought you were telling me it should be linear.

The question I am asked is...What I would expect "n" to be. Well I would expect it to be other than 1 because it is not a linear relationship ,the potential difference decreases with the first power of the distance. such as V=kQ/r

but is there a way I can calculate an n value? as I need to compute percent error and I need to find an actual value being the experimental value is given by excel?

Thanks for the help I think I was trying to make more out of what I was being asked.
 
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  • #6


also would the slope of the trend-line represent the constant value k? I plotted both V to r and and also the magnitude of E to R and I get a slope of aprox... 8.77 which seems close to the k value of 8.99*10^9 ?
 
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1. What is the significance of n in the power function?

N in the power function represents the power or exponent to which the independent variable (distance) is raised. It affects the shape and steepness of the curve in the potential vs distance graph.

2. How is n determined in the power function?

N can be determined by fitting the power function to the graph using a regression analysis. This involves finding the best-fit line that minimizes the sum of the squared differences between the actual data points and the predicted values from the power function.

3. What does a higher value of n indicate in the power function?

A higher value of n indicates a steeper curve in the potential vs distance graph, meaning that small changes in distance will result in larger changes in potential. This could suggest a stronger relationship between the variables and a higher degree of dependence.

4. How does n affect the accuracy of the power function fit?

The value of n can greatly affect the accuracy of the power function fit. If n is chosen without proper analysis or understanding of the data, it could result in a poor fit and inaccurate predictions. It is important to choose the appropriate value of n based on the data and the relationship between the variables.

5. Can n have a negative value in the power function?

Yes, n can have a negative value in the power function. This would result in an inverse relationship between the variables, where an increase in distance would lead to a decrease in potential. It is important to consider the physical meaning and implications of a negative value of n when fitting the power function to a graph.

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