Dielectric hysteresis loss in a cable varies as

Question

Examoogle · Accepted Answer

The correct answer is Option B: (Impressed voltage)$^2$. Dielectric hysteresis loss in an underground cable is the power dissipated as heat due to the molecular friction caused by the alternating electric field in the cable's insulation. This loss is directly proportional to the square of the applied (impressed) voltage ($V^2$), frequency ($f$), capacitance ($C$), and the dielectric loss angle ($ an \delta$).

Step-by-Step Solution & Concepts:
Dielectric hysteresis loss in an underground cable is the power dissipated as heat due to the molecular friction caused by the alternating electric field in the cable's insulation. This loss is directly proportional to the square of the applied (impressed) voltage ($V^2$), frequency ($f$), capacitance ($C$), and the dielectric loss angle ($ an \delta$).

Working Principle: When an AC voltage is applied across a dielectric material, the dipoles within the material attempt to align with the changing polarity of the electric field. Because the dielectric response is not instantaneous, a phase lag occurs, resulting in the dissipation of energy in the form of heat during each cycle of the alternating voltage. Mathematically, this loss is given by $P_d = V^2 \omega C 	an \delta$.

Key Formulas: $P_d = V^2 \cdot 2\pi f \cdot C \cdot 	an \delta$ — The expression for dielectric loss where $P_d$ is the loss in Watts, $V$ is the impressed voltage, $f$ is frequency, $C$ is capacitance, and $	an \delta$ is the loss factor.; $P_d \propto V^2$ — Relationship showing dielectric loss varies with the square of the voltage.

Key Points: Dielectric loss is primarily a property of the insulation material (e.g., XLPE, PILC).; It contributes to the heating of the cable, which limits the current-carrying capacity (ampacity) of the cable.; Higher voltages lead to significantly higher dielectric losses, which is a major design consideration for high-voltage (HV) and extra-high-voltage (EHV) cables.; The power factor of the insulation is related to $	an \delta$.

Advantages: Helps in selecting proper insulation material for specific voltage ratings.; Allows engineers to calculate thermal limits and derating factors for cables.

Disadvantages: Increased energy loss at higher voltage levels.; Causes internal heating which can lead to degradation of insulation over time (dielectric breakdown).

Applications: Design and insulation coordination of underground power transmission cables.; Predictive maintenance for testing insulation quality using power factor testing.

Additional Info: The loss factor $	an \delta$ is also known as the dissipation factor.. Option B is the correct choice because $P_d$ is mathematically derived to be proportional to the square of the voltage applied across the dielectric.

Answer: B is correct — Dielectric hysteresis loss in a cable is directly proportional to the square of the impressed voltage ($V^2$).

Exam Tip: Always remember that while dielectric loss is proportional to $V^2$, the charging current of the cable is directly proportional to $V$. Do not confuse the two.

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Option A: Impressed voltage

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Option C: (Impressed voltage)$^{1/2}$

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Option D: (Impressed voltage)$^{3/2}$

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