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GATE 2014 EE (EE2) – Question 52

Power Systems · Basic concepts of electrical power generation, AC and DC transmission concepts, Models and performance of transmission lines and cables · 2 marks · Multiple choice

Two horizontal conductors of a 50 Hz single-phase line have outer diameter 1.6 cm and center spacing 6 m. Given $\epsilon_0=8.854\times10^{-12}$ F/m, find capacitance to ground per conductor per kilometre.

  1. $4.2\times10^{-9}$ F
  2. $8.4\times10^{-9}$ F
  3. $4.2\times10^{-12}$ F
  4. $8.4\times10^{-12}$ F

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Correct answer: (B) $8.4\times10^{-9}$ F

Explanation

The conductor radius is0.008m and spacing is6m. For the two-wire line,the neutral-referenced capacitance per conductor is Cn=2πε0/ln(D/r). Substitution gives2π(8.854×10^−12)/ln750≈8.403×10^−12F/m. Multiply by1000to get **8.4×10^−9F/km,B**. Line-to-line capacitance would be half this value.