A particular load has a PF of 0.8 lagging. The power...

A particular load has a PF of 0.8 lagging. The power delivered to the load is $40 \mathrm{~kW}$ from a $220 \mathrm{~V} \mathrm{rms} 60 \mathrm{~Hz}$ line. If the transmission line resistance is $0.085 \Omega$, determine the real power that must be generated at the supply.

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Key Concepts

Power Factor

Power factor represents the ratio of real power (which performs work) to apparent power (the product of the circuit’s voltage and current). It reflects how effectively the current is being converted into useful work and is crucial in AC power systems. A lower power factor indicates that more apparent power must be supplied to deliver the same amount of real power, leading to increased losses in the system.

Apparent Power

Apparent power is the product of the RMS voltage and current in an AC circuit, representing the total power that flows in the circuit regardless of how much of it is actually used for work. It combines both the real (active) power and the reactive power and must be higher than the real load power when the power factor is less than one. This concept is essential when calculating the required current and subsequently the losses in the transmission medium.

Transmission Line Losses

Transmission line losses occur due to the resistance present in the conductors that carry electrical power from the supply to the load. These losses are typically calculated using the I²R formula, where the current is derived from the apparent power. Understanding and accounting for these losses is essential for determining the total power that must be generated to ensure the load receives the required amount of power.

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