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 270 -V $\mathrm{ms} 60$ -Hz line. What value of capacitance placed in parallel with the load will raise the pf to 0.9 lagging?

Key Concepts

Power Factor

Power factor is the ratio of real power (the component of power that does work) to apparent power (the vector sum of real and reactive power) in an AC electrical system. It is defined as the cosine of the phase angle between the voltage and the current waveforms. A lagging power factor indicates that the current lags behind the voltage, typical in inductive loads.

Reactive Power

Reactive power is the component of electrical power that oscillates between the source and the reactive elements in the load, such as inductors or capacitors. It does not perform any real work but is necessary for the functioning of AC systems. The reactive power contributes to the overall apparent power and affects the efficiency of the system.

Power Factor Correction

Power factor correction is the process of adjusting the power factor of a load from its current value to a desired value by adding devices such as capacitors or inductors. In networks with inductive loads, adding a capacitor in parallel can supply leading reactive power, which offsets the lagging reactive power of the load, thus improving the overall power factor.

Capacitor Sizing

Capacitor sizing involves calculating the required capacitance to supply the reactive power necessary to achieve the desired power factor. This is typically done by first determining the reactive power difference between the original and target power factors, and then using the relationship between reactive power, voltage, frequency, and capacitance to compute the appropriate capacitor value.

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