The power company must generate 100 kW to supply an...

The power company must generate $100 \mathrm{kW}$ to supply an industrial load with $94 \mathrm{kW}$ through a transmission line with $0.09-\Omega$ resistance. If the load power factor is 0.83 lagging, find the load voltage.

Key Concepts

Phasor Analysis in AC Circuits

Phasor analysis is a technique used in AC circuit analysis that represents sinusoidally varying voltages and currents as vectors (phasors) in the complex plane. This approach simplifies the process of analyzing the phase relationships between various quantities like voltage, current, and impedance, making it easier to tackle problems involving power generation, transmission losses, and load voltages in AC systems.

Power Factor

Power factor is the cosine of the phase angle between the voltage and current waveforms in an AC system, and it indicates the efficiency with which the electrical power is being converted into useful work. A lagging power factor, common in inductive loads, implies that the current lags the voltage, necessitating corrections or adjustments in circuit calculations to accurately account for the real power delivered versus the apparent power drawn.

Complex Power

Complex power is a fundamental concept in AC circuit analysis that combines both real power (which does actual work) and reactive power (which oscillates between source and load) into a single complex quantity denoted by S = P + jQ. It provides a comprehensive description of how energy is consumed or supplied in AC systems, and is particularly useful when analyzing circuits with loads that are not purely resistive.

Transmission Line Voltage Drop

Transmission line voltage drop refers to the reduction in voltage that occurs as electrical power is transmitted through conductors with inherent resistance. Ohm’s law is applied in the AC context, often using phasor analysis, to determine the drop (I·R) across the line's resistance, impacting the voltage available at the load and playing a crucial role in power system design and operation.

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