Capacitance of a cylindrical capacitor

In summary, the conversation revolved around calculating the capacitance per meter for a coaxial cable with given inner and outer radii and filled with polystyrene. The equation used was C=\frac{2*pi*E*K}{ln(b/a)}, and after converting units and plugging in values, the initial answer was incorrect. Upon further review, it was determined that the correct answer is 98.596 pF/m.
  • #1
stosw
21
0

Homework Statement



A coaxial cable used in a transmission line has an inner radius of 0.15 mm and an outer radius of 0.65 mm. Calculate the capacitance per meter for the cable. Assume that the space between the conductors is filled with polystyrene. (Also assume that the outer conductor is infinitesimally thin).


Homework Equations



C=[tex]\frac{2*pi*E*K}{ln(b/a)}[/tex]

The Attempt at a Solution



After converting mm to m and plugging in values (used K = 2.6 for capacitance per meter) I got 551.05 pF/m.

Webassign has told me this is incorrect. Could someone point me where I went wrong?
 
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  • #2
I get a completely different answer when I plug the numbers in. Try showing your work here so we can see where your error is.
 
  • #3
Thanks.
Guess I should be more careful when using a calculator.

Correct answer is 98.596 pF/m
 

1. What is capacitance?

Capacitance is a measure of the ability of a capacitor to store electrical charge. It is measured in units of farads (F).

2. How is the capacitance of a cylindrical capacitor calculated?

The capacitance of a cylindrical capacitor can be calculated using the formula C = 2πε0εrL/ln(b/a), where C is the capacitance, ε0 is the permittivity of free space, εr is the relative permittivity of the material between the plates, L is the length of the capacitor, and a and b are the radii of the inner and outer cylinders, respectively.

3. What factors affect the capacitance of a cylindrical capacitor?

The capacitance of a cylindrical capacitor is affected by the distance between the cylinders, the relative permittivity of the material between the plates, and the length and size of the cylinders.

4. How does the capacitance of a cylindrical capacitor compare to other types of capacitors?

The capacitance of a cylindrical capacitor is typically higher than that of other types of capacitors, such as parallel plate capacitors, due to its larger surface area for charge storage.

5. How can the capacitance of a cylindrical capacitor be increased?

The capacitance of a cylindrical capacitor can be increased by decreasing the distance between the cylinders, increasing the length of the cylinders, and using a material with a higher relative permittivity between the plates.

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