Capacitance of a High Voltage cable.

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Joined Jan 3, 2014
I haven't done this in a while so I would be grateful if someone could check my answer. The question states a high voltage single phase cable consists of a:

i) Central copper conductor of diameter 4.8 cm.
ii) Insulating layer of XPLE of thickness 2.3 cm and relative permittivity k = 2.2.
iii) Conducting lead sheath of thickness 2.9 mm.
iv) Insulating HDPE layer of thickness 5 mm and k = 2.4.
v) Outer coating negligible thickness in contact with soil.

Find the capacitance of the two insulating layer per meter of cable length?

My attempt:

Permittivity of free space epsilon_0 = 8.8x10^-12;

Capacitance of a cylinder: \( C = \frac{2\pi k \epsilon_0}{ln(b/a)}\)

Capacitance of XPLE layer:

\( C = \frac{2\pi * 2.2 * 8.8x10^{-12}}{ln(0.071/0.048)} = 310.73x10^{-12} F/m\)

Capacitance of HDPE:

\( C = \frac{2\pi * 2.4 * 8.8x10^{-12}}{ln(0.0789/0.0739)} = 2.03x10^{-9} F/m\)

The reason I'm unsure is that it seems too simple for what the question asks. Have I done this right of am I missing something.
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