Capacitance of a cylindrical capacitor

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SUMMARY

The capacitance per meter of a coaxial cable with an inner radius of 0.15 mm and an outer radius of 0.65 mm, filled with polystyrene, is calculated using the formula C = (2 * π * E * K) / ln(b/a). The correct capacitance value is 98.596 pF/m, contrasting with the incorrect calculation of 551.05 pF/m. The error arose from miscalculating or misapplying the formula, particularly in the logarithmic term or the dielectric constant.

PREREQUISITES
  • Understanding of coaxial cable geometry
  • Familiarity with capacitance formulas
  • Knowledge of dielectric materials, specifically polystyrene
  • Basic proficiency in logarithmic calculations
NEXT STEPS
  • Review the derivation of the capacitance formula for coaxial cables
  • Study the properties and applications of polystyrene as a dielectric material
  • Practice logarithmic calculations in the context of electrical engineering
  • Explore the impact of different dielectric constants on capacitance values
USEFUL FOR

Electrical engineering students, physics students, and professionals involved in designing or analyzing transmission lines and capacitive components.

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

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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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.
 
Thanks.
Guess I should be more careful when using a calculator.

Correct answer is 98.596 pF/m
 

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