An industrial plant consumes 75 kW at 0.84 Pf lagging when connected to a 220 ∠0^∘ V rm 60 Hz

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An industrial plant consumes 75 kW at 0.84 Pf lagging when...

An industrial plant consumes $75 \mathrm{~kW}$ at $0.84 \mathrm{Pf}$ lagging when connected to a $220 \angle 0^{\circ} \mathrm{V}$ rm $60 \mathrm{~Hz}$ line. Determine the value of the capacitance, which, when placed in parallel with the load, will raise the power factor to $0<$ lagging.

Key Concepts

Power Factor

Power factor is the cosine of the phase angle between the voltage and current in an AC circuit. It quantifies the efficiency of power utilization, representing the ratio of useful (real) power to the apparent power. A low power factor indicates a significant proportion of reactive power, which does not perform useful work but contributes to the current flow in the system.

Reactive Power

Reactive power is the component of AC power that oscillates between the source and reactive components (inductors and capacitors) in the circuit. Measured in VARs (volt-ampere reactive), it is responsible for establishing the electric and magnetic fields necessary for the operation of these devices, but does not contribute to actual work output. Managing reactive power is crucial for efficient power system operation.

Apparent Power

Apparent power is the combination of real power and reactive power and is measured in VA (volt-amperes). It represents the total power that must be supplied to meet both the work performing and reactive requirements of a circuit. The relationship between real, reactive, and apparent power is typically expressed using a power triangle.

Power Factor Correction

Power factor correction involves the adjustment of the load’s apparent power to decrease the reactive component, thereby improving the power factor. This is typically achieved by adding capacitors or inductors to the circuit. In the case of a lagging power factor, capacitors are used to supply leading reactive power which counteracts the inductive effects, mitigating losses and improving efficiency.

Capacitor Behavior in AC Circuits

In AC circuits, capacitors store and release energy in the form of an electric field, providing a leading reactive current. This particular behavior makes them effective for power factor correction. The reactive power supplied by a capacitor is determined by its capacitance, the voltage across it, and the frequency of the AC supply. The relationship is expressed as Qc = V^2?C, where ? is the angular frequency.

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