Parallel plate capacitor and insulating material

[tarellan]

Homework Statement

A parallel-plate capacitor has plates of 10 cm^2 area separated by a 0.10mm layer of glass insulation with resistivity rho = 1.2x10^13 omega*m and dielectric constant k= 5.6. Because of the finite resistivity, current can leak through the insulation.

How do I Show that it depends only on the properties of the insulating material and not on its dimensions?

Homework Equations

C= emf(A/d)

The Attempt at a Solution

I found the time constant for this capacitor to discharge through its insulation. T= 590s

 

[LowlyPion]

Homework Statement

A parallel-plate capacitor has plates of 10 cm^2 area separated by a 0.10mm layer of glass insulation with resistivity rho = 1.2x10^13 omega*m and dielectric constant k= 5.6. Because of the finite resistivity, current can leak through the insulation.

How do I Show that it depends only on the properties of the insulating material and not on its dimensions?

Homework Equations

C= emf(A/d)

The Attempt at a Solution

I found the time constant for this capacitor to discharge through its insulation. T= 590s

Consider the resistivity

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html#c2

Consider too the equation you have for capacitance.

Notice anything about how - when you combine the 2 - the RC has a tendency not to be dependent on the cross sectional area?

 

[nlightner]

I would first clarify the question and make sure I understand what is being asked. The question is asking how to show that the leakage current through the insulation of a parallel plate capacitor depends only on the properties of the insulating material and not on the dimensions of the capacitor.

To answer this question, I would first remind the student that the leakage current is directly related to the resistivity of the insulating material. This means that the higher the resistivity, the lower the leakage current will be. Therefore, the properties of the insulating material, such as resistivity, play a crucial role in determining the leakage current.

Next, I would explain that the dimensions of the capacitor, such as the area of the plates and the distance between them, do not directly affect the resistivity of the insulating material. The resistivity is an intrinsic property of the material and is not affected by the size or shape of the capacitor. Therefore, the dimensions of the capacitor do not play a role in determining the leakage current.

To further illustrate this point, I would use the formula for capacitance, C= emf(A/d), where emf is the permittivity of free space, A is the area of the plates, and d is the distance between the plates. This formula shows that the capacitance of a parallel plate capacitor is directly proportional to the area of the plates and inversely proportional to the distance between them. However, the resistivity of the insulating material is not included in this formula, further emphasizing that it is not affected by the dimensions of the capacitor.

In conclusion, the leakage current through the insulation of a parallel plate capacitor depends only on the properties of the insulating material, such as resistivity, and not on the dimensions of the capacitor. This is because the resistivity is an intrinsic property of the material and is independent of the size or shape of the capacitor.