The breakdown of insulation of a cable can be avoided economically by using

Question

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The correct answer is Option C: Either (a) or (b). To achieve uniform stress distribution within the insulation of a high-voltage cable, the potential gradient must be maintained at a constant level. Both grading with different dielectrics (capacitance grading) and the use of inter-sheaths serve to reduce the maximum electric stress, preventing insulation breakdown economically.

Step-by-Step Solution & Concepts:
To achieve uniform stress distribution within the insulation of a high-voltage cable, the potential gradient must be maintained at a constant level. Both grading with different dielectrics (capacitance grading) and the use of inter-sheaths serve to reduce the maximum electric stress, preventing insulation breakdown economically.

Working Principle: The electric stress $g(x)$ at any point $x$ from the center of a single-core cable is given by $g(x) = \frac{V}{x \ln(R/r)}$. Since stress is highest at the conductor surface ($x=r$), we either introduce layers of different permittivities $\epsilon$ such that $\epsilon_1 g_1 = \epsilon_2 g_2$ (capacitance grading) or place metallic inter-sheaths at specific radii maintained at calculated potentials to break the large voltage drop into smaller, manageable steps.

Key Formulas: $g_{max} = \frac{V}{r \ln(R/r)}$ — Maximum stress at conductor surface; $V = \int_{r}^{R} g(x) dx$ — Potential distribution across insulation

Key Points: Stress is inversely proportional to the radius $x$.; Capacitance grading uses layers with decreasing permittivity $\epsilon$ from center to sheath.; Inter-sheaths divide the total potential $V$ into intermediate potentials $V_1, V_2, ...$ using a transformer or voltage divider.; Grading allows the use of thinner insulation for the same operating voltage.

Advantages: Reduces the required thickness of insulation; Increases the current-carrying capacity of the cable; Prevents dielectric breakdown at the conductor surface

Disadvantages: Capacitance grading is complex to manufacture; Inter-sheaths require external voltage control equipment; Increased risk of insulation failure at inter-sheath joints

Applications: High-voltage (HV) underground transmission lines; Submarine power cables

Additional Info: For capacitance grading, the condition is $\epsilon_1 r_1 = \epsilon_2 r_2 = \epsilon_3 r_3 = constant$.. Option B (Inter-sheath) is valid, but since Option A is also a correct method of grading, Option C is the most comprehensive answer.

Answer: C is correct — Both capacitance grading and inter-sheath grading are proven techniques to minimize the maximum potential gradient and prevent insulation failure economically.

Exam Tip: Always remember: $g_{max}$ occurs at the surface of the core ($x=r$). Any method that reduces this value or makes the stress profile flat is considered a 'grading' technique.

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Option A: Insulation layer of different dielectrics

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Option B: Inter sheath

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Option D: None of above

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