A plant consumes 20 kW of power from a 240-V rms line. If...

A plant consumes $20 \mathrm{kW}$ of power from a $240-\mathrm{V}$ rms line. If the load power factor is 0.9 lagging, what is the angle by which the load voltage leads the load current? What is the load current phasor if the line voltage has a phasor of $240\underline{/0_{\circ}}V rms?$

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Key Concepts

AC Power Calculation

In AC circuits, the real power is calculated as the product of the voltage, the current, and the cosine of the phase angle (P = V * I * cos?). This relationship is essential for finding unknown circuit parameters, such as current, when the voltage, real power, and power factor are known, thereby enabling proper design and analysis of power systems.

Power Factor

The power factor in an AC circuit is the cosine of the phase angle between the voltage and current waveforms. It represents the ratio of the actual (real) power consumed by the load to the apparent power and indicates how effectively the electrical power is being used. A lagging power factor means that the current lags behind the voltage, which has significant implications for energy efficiency.

Phasor Representation

Phasors are a mathematical tool used to represent sinusoidal functions in the complex plane, encapsulating both magnitude and phase angle. This representation simplifies the analysis of AC circuits by converting differential equations into algebraic equations, making it easier to handle calculations involving resonance, impedance, and phase differences.

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