The capacitance of a cable depends upon

Question

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The correct answer is Option D: All of above. The capacitance of an underground cable is defined by its physical geometry and the properties of the insulating material. Since it follows the principle of a cylindrical capacitor, it is directly proportional to the length and relative permittivity, and inversely proportional to the logarithmic ratio of the sheath-to-core radii.

Step-by-Step Solution & Concepts:
The capacitance of an underground cable is defined by its physical geometry and the properties of the insulating material. Since it follows the principle of a cylindrical capacitor, it is directly proportional to the length and relative permittivity, and inversely proportional to the logarithmic ratio of the sheath-to-core radii.

Working Principle: A cable acts as a cylindrical capacitor where the core is the inner electrode and the metallic sheath is the outer electrode. The capacitance $C$ is determined by the formula $C = \frac{2\pi \epsilon_0 \epsilon_r l}{\ln(D/d)}$, where $\epsilon_r$ is the relative permittivity, $l$ is the length, $D$ is the sheath diameter, and $d$ is the core diameter.

Key Formulas: $C = \frac{2\pi \epsilon_0 \epsilon_r l}{\ln(\frac{D}{d})}$ — Capacitance of a single-core cable; $\epsilon = \epsilon_0 \epsilon_r$ — Permittivity of the dielectric medium

Key Points: Capacitance increases linearly with the length ($l$) of the cable.; Higher relative permittivity ($\epsilon_r$) of the insulation leads to higher charging currents.; The ratio of diameters ($D/d$) dictates the geometric factor of the capacitor.; Underground cables have much higher capacitance than overhead lines due to the proximity of the sheath and the dielectric medium.

Advantages: Used for transmitting power in congested urban areas.; Provides reliable operation without environmental interference.

Disadvantages: High charging current due to significant capacitance.; Complex thermal management required compared to overhead lines.

Applications: Underground power distribution; Submarine power cables

Additional Info: The charging current $I_c = j\omega C V$ becomes significant in long HV cables, requiring shunt reactor compensation.. Option A, B, and C are all individual variables in the capacitance equation, thus D is the only complete answer.

Answer: D is correct — The capacitance of a cable depends on its length, the dielectric material used, and the geometric configuration of the core and sheath.

Exam Tip: Always remember that in power systems, cable charging current is a major factor in determining the maximum transmission distance for underground AC cables.

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Option A: The length of the cable

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Option B: Relative permittivity of dielectric used in cable

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Option C: Ratio of sheath diameter and core diameter

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