Explanation of capacitance formula

In summary, π appears as a constant in capacitance equations due to the way units are written. Gaussian units use 4 pi, while similar unit systems use 8.85*10^-12.
  • #1
Niaboc67
249
3
Hello, I am new to electronics and am having trouble understanding this formula for capacitance:

7cgnZPY.png


Could someone please break this down into layman terms? Interestingly π appears? I'd like to understand why that exists in capacitance.

Thank you all in advance!
 
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  • #3
Actually, that equation you got is very strange... 8.85*10^-12 looks like the value for vacuum permittivity (in F/m) in SI units, but I think that 4pi is wrong. Where did you get that equation?
 
  • #4
Thank you for the replies thus far. I got the image from this video at 1:05:
I was wondering how I could make a capacitor from scratch. I am only up to pre-calculus so not entirely well-versed in mathematical reasoning yet.
 
  • #5
Yes, I think he mixed up his units..

Basically..

##C = ε * \frac{A}{d}##

where ε is a constant. The form of the constant depends on the unit system used.

http://en.wikipedia.org/wiki/Capacitance

In CGS units the equation has the form:[2]
2884456a177ca663f706bb41c56182a1.png
He seems to have used the SI value for ε0
 
  • #6
Niaboc67 said:
Hello, I am new to electronics and am having trouble understanding this formula for capacitance:

7cgnZPY.png


Could someone please break this down into layman terms? Interestingly π appears? I'd like to understand why that exists in capacitance.

Thank you all in advance!
I think that's asking a bit too much. It's not a "layman's" subject. Unless you want to get into EM theory at some depth then it's quite OK just to use the formula (subject to it being the correct on - see the other posts. The nearest thing to helping you is to say that the Capacitance will be proportional to the total area (double the area = double the Capacitance) and inversely proportional to the spacing (double the spacing = half the Capacitance). The rest of the formula can be treated as 'just constants', which will give you the right answer in Farads. (I am not being snobby about this - many brilliant Engineers are prepared to do this and use formulas that they don't fully understand - in the same way that they used equipment that they could never hope to build for themselves)
BTW π appears all over the place in Science and Maths. The bit about the area of a circle is only one of the many places you will find π - it is just the most familiar example :).
 
  • #7
Thank you all for the replies...I've got a lot to learn. I guess when in doubt consult wikipedia. π and phi and all constants are becoming particularly puzzling for me. For the sheer fact that a constant that relates to all things exists makes me think the universe was programmed...or the multiverse must be accurate. Sorry for being so tangential.
 

Related to Explanation of capacitance formula

1. What is capacitance?

Capacitance is a measure of an object's ability to store electrical energy. It is the ratio of the electric charge stored on an object to the potential difference (voltage) between the object's plates.

2. What is the formula for capacitance?

The formula for capacitance is C = Q/V, where C is capacitance, Q is charge, and V is voltage. It can also be written as C = εA/d, where ε is the permittivity of the material between the plates, A is the area of the plates, and d is the distance between the plates.

3. How is capacitance measured?

Capacitance is typically measured using a device called a capacitance meter. This device applies a known voltage to the plates of the capacitor and measures the resulting charge. The capacitance can then be calculated using the formula C = Q/V.

4. What factors affect capacitance?

Capacitance is affected by the area of the plates, the distance between the plates, and the type of material between the plates (permittivity). The closer the plates are together, the larger the capacitance will be. Similarly, a larger plate area and a higher permittivity material will result in a larger capacitance.

5. What are some real-life applications of capacitance?

Capacitance is used in a wide range of electronic devices, such as radios, televisions, and computers. It is also used in power factor correction to improve the efficiency of electrical systems. Capacitors are also commonly used in electric circuits to store energy and regulate voltage.

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