Capacitance Formula

The capacitance of a cable is calculated as follows:

• C = ε / (18 × ln(r2 / r1))
  

Where:

• C: Capacitance of the cable (µF/km)
  
• ε: Relative permittivity of the insulation material (dimensionless)
  
• r1: Radius at the surface of the conductor screen or conductor diameter (mm)
  
• r2: Radius at the surface of the insulation or insulated diameter (mm)
  

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Key Notes:

• ε (Relative Permittivity): This represents the dielectric constant of the insulation material. For XLPE (cross-linked polyethylene), the typical value is:
    ε = 2.5 (from IEC 60287 standards).
  
• ln(r2 / r1): The natural logarithm of the ratio of the outer insulation radius (r2) to the conductor radius (r1).
  
• The constant 18 ensures the result is in microfarads per kilometer (µF/km).
  

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Application

The capacitance of a cable affects:

• The charging current in the cable.
• Voltage regulation in long cables.
• Power losses and insulation stress due to stored energy.

This formula is widely used in cable design to determine insulation thickness and ensure compliance with industry standards like **IEC 60287**.

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Example Calculation

**Given Data:**

• ε = 2.5 (for XLPE insulation)
  
• r1 = 10 mm
  
• r2 = 30 mm
  

**Steps:**

• Calculate the natural logarithm:

ln(r2 / r1) = ln(30 / 10) = ln(3) ≈ 1.0986

• Substitute values into the formula:

C = 2.5 / (18 × 1.0986)
  C ≈ 2.5 / 19.7748
  C ≈ 0.1264 µF/km
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**Result:** The capacitance of the cable is approximately **0.1264 µF/km**.

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Conclusion

This formula is essential for understanding the electrical behavior of cables in power systems, particularly in high-voltage applications. It helps engineers ensure proper insulation design and minimize losses in long-distance power transmission.