Finding the Thickness of Polystyrene in a Capacitor

[warnexus]

Homework Statement

Homework Equations

Capacitance = k(epsilon zero) (Area) / (distance)

Length (thickness) = (Volt)(Area) / (Current * Resistivity)

The Attempt at a Solution

Given:

Capacitance : 480 * 10 ^ -12 Farad
Radius: 24 * 10 ^ - 2 m
Area: pi * r ^ 2
dielectric constant of polystyrene: 2.6
breakdown field(MV/m) : 25
Resistivity of Polystyrene : 10 ^ 15

distance = (2.6)(8.85 * 10 ^ -12) (3.14 * (24* 10 ^ -2) ^ 2) / (480 * 10 ^ -12)

however finding the distance does not seem to help me at all since the other equation do not involve distance

any guidance would help

 

[TSny]

distance = (2.6)(8.85 * 10 ^ -12) (3.14 * (24* 10 ^ -2) ^ 2) / (480 * 10 ^ -12)

Hello. What distance does this represent physically?

 

[warnexus]

distance apart for two capacitors

 

[TSny]

I guess you mean the distance between the two circular plates of the capacitor. (You only have one capacitor.)

But isn't this the same as the thickness of the polystyrene?

 

[warnexus]

oh so that's what they mean! now that I think about you have a point there. so length, spacing, distance,thickness are same ideas. thanks for the guidance

 

[TSny]

Yes. It's always important to know what the symbols in an equation represent.

 

[warnexus]

Yes. It's always important to know what the symbols in an equation represent.

I was wondering. I need to find voltage of the capacitor. I do not know the current.

resistance = (resistivity)(length)/(pi * (r)^ 2)

I wind up finding the resistance which turned out to be 4793.7 ohms or 4793 ohms

but current is still missing.

current = (voltage)/(resistance)

voltage = (dielectric constant)(epsilon zero) (Current)(Resistivity)/(Capacitance)

or

I could have found voltage a different way

voltage = (Charge)/(Capacitance)

but no information about what charge is within the capacitor

 

[haruspex]

It's a capacitor; you do not want current.
What do you take the term 'breakdown voltage' to mean?

 

[warnexus]

It's a capacitor; you do not want current.
What do you take the term 'breakdown voltage' to mean?

failure of an electrical circuit

well i did list the polystyrene breakdown field to be 25 * 10 ^ 6 V/m

oh now I get it! multiply the thickness by the breakdown voltage and viola working voltage. thanks haruspex!

 

[haruspex]

failure of an electrical circuit

But what specifically in relation to capacitors?

well i did list the polystyrene breakdown field to be 25 * 10 ^ 6 V/m

Yes, but you did not use it.

I know the electric field = (Volt)/(Area)

So what would the breakdown voltage be for this capacitor?

 

[warnexus]

But what specifically in relation to capacitors?

Yes, but you did not use it.

So what would the breakdown voltage be for this capacitor?

failure of an electrical field from a capacitor

i modify the content of my previous post. the electric field equation Electrical Field = (Volt/Area) would not work. I just wind up using the answer I got for thickness and used it with the breakdown voltage and found voltage that way.

 

[haruspex]

failure of an electrical field from a capacitor

No, it would be the capacitor passing a DC current, which it is not supposed to do.

I just wind up using the answer I got for thickness and used it with the breakdown voltage and found voltage that way.

Let's get the terminology right: you used the breakdown field and the polystyrene thickness to find the breakdown voltage, which is the 'working voltage' required, yes?