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Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
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With the rise in temperature, the insulation resistivity
Remains unchanged
Decrease linearly
Increases linearly
Reduces exponentially
Reduces exponentially
The insulation resistivity of electrical cables decreases exponentially as the operating temperature increases. This occurs because heat facilitates greater molecular mobility and ionization within the dielectric material, leading to a higher leakage current.
The insulation resistivity of electrical cables decreases exponentially as the operating temperature increases. This occurs because heat facilitates greater molecular mobility and ionization within the dielectric material, leading to a higher leakage current.
╧Б(T)=╧Б0тАЛeтИТ╬▒T тАФ The relationship between resistivity ╧Б and temperature T, where ╬▒ is the temperature coefficient.
R=╧БAlтАЛ тАФ Basic resistance formula showing direct dependence on resistivity.
In insulating materials, the conduction process is governed by the thermal excitation of charge carriers. As temperature rises, the concentration and mobility of these carriers increase following the Arrhenius relationship. Mathematically, the resistivity follows the form ╧Б=╧Б0тАЛeтИТ╬▒T, demonstrating that insulation effectiveness degrades significantly with thermal stress.
Insulating materials (dielectrics) exhibit a negative temperature coefficient of resistance.
Excessive temperature rise leads to 'Thermal Runaway' in cables, potentially causing insulation breakdown.
The exponential decline makes heat dissipation a critical design factor in power cables.
This phenomenon is distinct from metallic conductors, which typically show an increase in resistivity with temperature.
Predictable failure modes under thermal overload
Allows engineers to specify appropriate thermal ratings (e.g., 90┬░C for XLPE)
Restricts current carrying capacity of cables in high-temperature environments
Accelerates insulation aging/brittleness
Power Cable Design (XLPE, PVC, EPR insulation)
Transformer winding insulation specification
High-voltage underground cables require sophisticated thermal management to prevent the exponential drop in resistivity from causing dielectric failure.
Option B (Decrease linearly) is incorrect because the atomic kinetics of dielectric breakdown follow an Arrhenius (exponential) dependence rather than linear.
D is correct тАФ The resistivity of insulating materials is inversely proportional to temperature through an exponential function, causing it to drop rapidly as cables heat up.
Always remember: Metals (conductors) have a positive temperature coefficient, whereas insulators and semiconductors have a negative temperature coefficient.