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The capacitance of a cable increases
Linearly with the increase in cable length
Linearly with the decrease in cable length
Exponentially with the increase in cable length
None of above
Linearly with the increase in cable length
The capacitance of a cable depends on its geometry and the permittivity of the insulation material. Since a cable acts as a cylindrical capacitor, its total capacitance is directly proportional to its length L.
The capacitance of a cable depends on its geometry and the permittivity of the insulation material. Since a cable acts as a cylindrical capacitor, its total capacitance is directly proportional to its length L.
C=ln(R/r)2╧А╧╡0тАЛ╧╡rтАЛLтАЛ тАФ Capacitance of a single-core cable
CтИЭL тАФ Linear relationship between capacitance and length
The capacitance of an underground cable is given by C=ln(R/r)2╧А╧╡0тАЛ╧╡rтАЛLтАЛ. As the length L of the cable increases, the surface area of the conductors in contact with the dielectric increases linearly, leading to a linear increase in the total capacitance of the cable.
Cable capacitance is a shunt parameter in power systems.
Higher capacitance leads to higher charging currents, which can affect voltage regulation in long cables.
The dielectric material (epsilonrтАЛ) significantly influences the total capacitance value.
Useful for calculating charging current in power transmission lines.
Helps in determining the reactive power compensation requirements.
High capacitance increases the charging current, which consumes thermal capacity of the cable.
Contributes to dielectric losses in HVAC cables.
Underground transmission and distribution power systems.
Submarine power cables for offshore wind farms.
The charging current IcтАЛ=VтЛЕ╧ЙC also increases linearly with the length of the cable.
Option B is incorrect because capacitance is an extensive property that increases with material volume/length, not a decreasing one.
A is correct тАФ The capacitance of a cable increases linearly as the length of the cable increases because CтИЭL.
Always remember that in transmission lines, capacitance (shunt) increases with length, whereas resistance and inductance (series) also increase with length.