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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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Active power is calculated by
VIcos∅
VIsin∅
VI
IR
VIcos∅
Active power (also known as real or true power) is the actual power dissipated in an AC circuit by the resistive components, measured in Watts. It is calculated by multiplying the RMS values of voltage (V), current (I), and the power factor (cosϕ), where ϕ is the phase angle between voltage and current.
Active power (also known as real or true power) is the actual power dissipated in an AC circuit by the resistive components, measured in Watts. It is calculated by multiplying the RMS values of voltage (V), current (I), and the power factor (cosϕ), where ϕ is the phase angle between voltage and current.
P=VIcosϕ — Formula for Active Power
Q=VIsinϕ — Formula for Reactive Power
S=VI — Formula for Apparent Power
In an AC circuit, the voltage and current may not be in phase due to reactive elements like inductors and capacitors. The instantaneous power p(t)=v(t)i(t) fluctuates, but the average power over a cycle is P=VIcosϕ. Only the resistive component of the load consumes real power, which is converted into heat or work, while the reactive components store and release energy without net consumption.
Active power represents the energy per unit time effectively utilized by the circuit.
The factor cosϕ is defined as the Power Factor of the circuit.
For a purely resistive circuit, ϕ=0, so cosϕ=1 and P=VI.
Active power is measured using a Wattmeter.
Useful for calculating actual electricity consumption (kWh).
Essential for sizing electrical equipment and power utility billing.
Does not account for energy stored in magnetic or electric fields.
Requires knowledge of phase shift to calculate accurately.
Electrical power systems monitoring.
Industrial energy auditing.
Appliance power rating standards.
Option B (VIsinϕ) represents Reactive Power, measured in VAR (Volt-Ampere Reactive).
Option C (VI) represents Apparent Power, measured in VA (Volt-Ampere).
Option D (IR) is physically incorrect in this context as it does not represent power (Power in a resistor is I2R).
A is correct — Active power is mathematically defined as the product of RMS voltage, RMS current, and the cosine of the phase angle between them, denoted as P=VIcosϕ.
In competitive exams, always remember: Active Power (P) uses cosine, Reactive Power (Q) uses sine, and Apparent Power (S) is the vector sum.