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Volume of copper required for an AC transmission line is inversely proportional
Current
Voltage
Power factor
All of above
Current
The volume of copper required in a transmission line is inversely proportional to the square of the transmission voltage, the square of the power factor, and is directly proportional to the power transmitted and length squared. Since options A, B, and C each contribute to the reduction of copper volume under various transmission constraints (like line losses or constant power delivery), the volume requirements are inherently linked to these parameters.
The volume of copper required in a transmission line is inversely proportional to the square of the transmission voltage, the square of the power factor, and is directly proportional to the power transmitted and length squared. Since options A, B, and C each contribute to the reduction of copper volume under various transmission constraints (like line losses or constant power delivery), the volume requirements are inherently linked to these parameters.
VтИЭV21тАЛ тАФ Volume is inversely proportional to the square of voltage
VтИЭ(cos╧Х)21тАЛ тАФ Volume is inversely proportional to the square of the power factor
I=3тАЛVcos╧ХPтАЛ тАФ Current relationship showing inverse dependence on voltage and power factor
The weight (or volume) of conductor material is determined by the cross-sectional area A required to carry current I within specified limits of power loss (I2R loss) and voltage regulation. Since I=3тАЛVcos╧ХPтАЛ, reducing the current (by increasing voltage V or power factor cos╧Х) significantly reduces the required conductor volume to maintain a constant percentage power loss.
Increasing voltage decreases the required current for a given power, leading to a smaller cross-sectional area of the conductor.
A lagging power factor increases the current for a given real power, necessitating a larger conductor size (higher volume).
Transmission efficiency improves significantly with higher voltage due to reduced I2R losses.
Copper volume is minimized when the power factor is maintained close to unity.
Higher transmission voltage reduces line losses.
Optimizing power factor minimizes infrastructure cost.
Higher voltages require more expensive insulation and corona prevention measures.
Low power factor loads necessitate additional compensation equipment like capacitor banks.
HVDC and HVAC high-voltage power transmission grids.
Industrial power factor correction units.
For a fixed percentage power loss, the weight of copper is inversely proportional to the square of the voltage.
Option A is correct because AтИЭI; Option B is correct because AтИЭV21тАЛ; Option C is correct because AтИЭcos2╧Х1тАЛ.
D is correct тАФ The volume of copper is inversely related to the square of the voltage and the square of the power factor, making all provided parameters critical to the conductor volume design.
Always remember that for constant power transmission, both voltage and power factor have a 'squared' inverse relationship with conductor volume, making them the most significant factors in economic grid design.