Explanation of capacitance formula

[Niaboc67]

Hello, I am new to electronics and am having trouble understanding this formula for capacitance:

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!

 

[Khashishi]

The 4 pi appears in Gaussian units, and similar unit systems where Gauss's law is given by
$\nabla \cdot \mathbf{E} = 4\pi \rho$
There is no 4 pi in the equation here:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/pplate.html

(I need to check if I got that backwards)

 

[Khashishi]

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?

 

[Niaboc67]

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.

 

[CWatters]

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]

He seems to have used the SI value for ε₀

 

[sophiecentaur]

Hello, I am new to electronics and am having trouble understanding this formula for capacitance:

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 :).

 

[Niaboc67]

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.