An industrial load that consumes 40 kW is supplied by the...

An industrial load that consumes $40 \mathrm{kW}$ is supplied by the power company, through a transmission line with $0.1-\Omega$ resistance, with $44 \mathrm{kW}$. If the voltage at the load is $240 \mathrm{V} \mathrm{rms}$, find the power factor at the load.

Key Concepts

Transmission Line Losses

Transmission line losses refer to the power that is dissipated as heat due to the resistance of the conductors in a power transmission system. These losses reduce the efficiency of power delivery and are important to consider when analyzing the overall power distribution and performance of electrical networks.

Apparent Power

Apparent power is the product of the RMS voltage and the RMS current in an AC circuit, typically measured in volt-amperes (VA). It represents the total power flow in the system, combining both the real power, which performs work, and the reactive power, which oscillates between the source and load.

RMS Voltage

RMS (Root Mean Square) voltage is a statistical measure of the magnitude of a varying voltage, and it is used to represent an equivalent DC value that delivers the same power. It is a fundamental parameter in AC circuit analysis, as it provides a measure of the effective voltage applied to a load.

Power Factor

Power factor is the ratio of the real power that does useful work to the apparent power that flows in an AC circuit. It indicates how effectively the electrical power is being converted into useful work output and is a critical parameter in power systems to assess efficiency and proper utilization of electricity.

Real Power

Real power, measured in watts (or kilowatts), is the actual power consumed by a load to perform work. It represents the energy conversion that occurs in the circuit and is the component of power that results in useful energy output, excluding energy that is temporarily stored and returned.

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