Capacitance vs. Inverse Distance Graph's Slope

In summary, the conversation discusses plotting a graph of capacitance and inverse distance, and determining the best fit equation and corresponding slope. The theoretical model for capacitance is mentioned as well. The equation provided in the attempt at a solution does not match the theoretical model, causing doubts about the accuracy of the slope. Any help in understanding the numerical value of the slope and determining the correct fit would be appreciated.
  • #1
Ayda
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Homework Statement


I plotted a graph where Capacitance is at y-axis and Inverse Distance is at x-axis. It looks like a positive, increasing function.
7ba61bc988a2022d108dde02e1a1b54e-full.png

I am asked of a best fit, also an equation. But i am not sure whether to use quadratic or linear fit. I am also asked of what the slope corresponds to. The plate area of the capacitor was kept constant, we only changed distance.

Homework Equations


y=2.8e-13*x+6.1e-12 Is the equation of a linear slope.

The Attempt at a Solution


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I thought the slope would correspond to electric permittivity. But now i have big doubts about it. I also assumed the slope would be a linear fit, but I am not sure. Also, what does the numerical value of slope in the equation would mean? Any help would be very much appreciated. Thank you.
 
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  • #2
The theoretical model is ##C = \epsilon * A/d##. (see https://www.electronics-tutorials.ws/capacitor/cap_4.html )
In the theoretical model, ##\epsilon * A## is related to your 2.8e-12, the ##1/d## is related to your x, and there is no constant term like your 6.1e-12.
 
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Likes Ayda
  • #3
FactChecker said:
The theoretical model is ##C = \epsilon * A/d##. (see https://www.electronics-tutorials.ws/capacitor/cap_4.html )
In the theoretical model, ##\epsilon * A## is related to your 2.8e-12, the ##1/d## is related to your x, and there is no constant term like your 6.1e-12.
Thank you so much.
 

FAQ: Capacitance vs. Inverse Distance Graph's Slope

1. What is capacitance?

Capacitance is the ability of a material or system to store an electric charge. It is measured in farads (F) and is represented by the symbol C.

2. How is capacitance related to distance?

The capacitance of a system is inversely proportional to the distance between its plates or electrodes. This means that as the distance between the plates decreases, the capacitance increases and vice versa.

3. What is the significance of the slope in a capacitance vs. inverse distance graph?

The slope of the capacitance vs. inverse distance graph represents the change in capacitance per unit change in distance. It can be used to calculate the capacitance value at a specific distance or to compare the capacitance of different systems.

4. How can the capacitance vs. inverse distance graph be used in practical applications?

The capacitance vs. inverse distance graph is commonly used in the design and analysis of capacitors, which are used in various electrical and electronic devices. It can also be used to determine the dielectric constant of a material or to optimize the distance between electrodes for maximum capacitance.

5. Are there any limitations to using the capacitance vs. inverse distance graph?

Yes, there are limitations to using the capacitance vs. inverse distance graph. It assumes that the material between the plates is a perfect dielectric and that the plates are parallel and of equal size. In real-world applications, these assumptions may not always hold true, resulting in deviations from the expected capacitance values.

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