What is the power factor of a cable of loss angle “ө”?

Explanation:

Power Factor of a Cable with Loss Angle “ө”

Definition: The power factor of a cable is a measure of the efficiency with which the electrical power is transmitted through the cable. It is the cosine of the angle between the voltage and current waveforms, also known as the phase angle. When dealing with a lossy cable, the loss angle “ө” is introduced, which represents the angle by which the current leads or lags the voltage due to the dielectric losses in the cable insulation.

Working Principle: The power factor in a cable is influenced by the dielectric properties of its insulation. The dielectric loss angle "ө" is related to the power factor by the sine function. The power factor is mathematically given as:

Power Factor = sin ө

Here, "ө" is the loss angle associated with the dielectric material of the cable. The sine function is used because the power factor is directly related to the losses occurring in the cable’s dielectric material. The higher the value of sin ө, the higher the losses, and consequently, the lower the efficiency of power transmission through the cable.

Correct Option Analysis:

The correct option is:

Option 1: sin ө

This option correctly defines the power factor of the cable in relation to the loss angle “ө.” The power factor is represented by the sine of the loss angle, which quantifies the contribution of dielectric losses in the cable. The sine function is appropriate because it accurately models the relationship between the loss angle and the power factor in lossy electrical systems.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: cos ө

This option represents the power factor of an ideal system where only the phase angle between voltage and current is considered, ignoring dielectric losses. In cables with dielectric losses, the power factor is not given by cos ө but by sin ө. Cos ө is relevant for systems where the inductive or capacitive reactance dominates without significant dielectric losses.

Option 3: tan ө

This option is not correct because tan ө represents the ratio of the reactive power to the active power in the system, not the power factor. While tan ө is related to the phase angle, it does not directly define the power factor of a lossy cable.

Option 4: Independent of ө

This option is incorrect because the power factor is directly dependent on the loss angle “ө.” The loss angle determines the extent of dielectric losses in the cable, which in turn affects the power factor. Therefore, it cannot be independent of “ө.”

Option 5: (No explanation provided in question)

This option does not provide any valid relation or definition for the power factor of a lossy cable. It is not relevant to the context of the question.

Conclusion:

Understanding the relationship between the loss angle “ө” and the power factor is crucial for analyzing the efficiency of power transmission in cables. The power factor, given by sin ө, accurately reflects the impact of dielectric losses on the system. This relationship is vital for designing and selecting cables with optimal performance characteristics. By minimizing the loss angle, the power factor can be improved, enhancing the overall efficiency of power transmission systems.