A single-core cable rated for 33000 V has a conductor diameter of 10 mm and an inner sheath diameter of 25 mm. The peak electrostatic stress within the cable is____________?
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Answer: B. 72 x 105 V/m
Explanation
Peak electrostatic stress in a single-core cable occurs directly at the surface of the central conductor. Calculating this maximum stress involves applying the logarithmic ratio of sheath to conductor radii. Mathematical evaluation of the given cable dimensions and voltage yields approximately seventy-two megavolts per meter. The electric field inside a coaxial cable varies inversely with the radial distance from the center. Conductor and sheath diameters determine the maximum electrostatic voltage gradient within the insulation. High voltage power cables require careful insulation grading to prevent localized dielectric breakdown.
Power transmission engineers calculate peak electrostatic stress to ensure underground cables operate safely. Exceeding the maximum stress rating of cable insulation can cause catastrophic underground power failures. Proper design prevents ionization and partial discharges within the insulating layers of high voltage lines. Option A is wrong because sixty-two megavolts per meter underestimates the calculated electrostatic stress. Option C is incorrect because eighty-two megavolts per meter overestimates the correct logarithmic calculation. Option D is incorrect because ninety-two megavolts per meter does not match the derived formula result.
- Subject
- Engineering
- Category
- Electrical Engineering
- Topic
- —
- Difficulty
- medium
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