Understanding Active Power: Formula, Measurement & Energy Efficiency

1. What is Active Power?

Active power (P) is the real power that performs useful work in an electrical circuit. It is the portion of electrical energy converted into:

✔ Mechanical work (motors, fans)
✔ Heat (heaters, ovens)
✔ Light (lamps, LEDs)

Unlike reactive power, which oscillates between source and load without doing useful work, active power is the real power consumed by electrical devices.

Example: A 1000W microwave consumes 1000 watts of active power to generate heat.

2. Active Power Measurement & Formula

Units of Measurement

Active power is measured in watts (W) and its multiples:

✔ 1 kW (kilowatt) = 1000 W
✔ 1 MW (megawatt) = 1,000,000 W
✔ 1 GW (gigawatt) = 1,000,000,000 W

Formulas for Active Power Calculation

1. For DC Circuits:

$$P = U \\\\times I$$

where:
✔ P – Active Power (W)
✔ U – Voltage (V)
✔ I – Current (A)

Example: If a battery supplies 12V and a lamp draws 5A, the active power is:

$$P = 12V \\\\times 5A = 60W$$

2. For AC Single-Phase Circuits:

$$P = U \\\\times I \\\\times \\\\cos\\\\varphi$$

✔ cos φ – Power factor (0 to 1), which indicates how efficiently power is used

Example: A 230V motor drawing 10A with a power factor of 0.9:

$$P = 230V \\\\times 10A \\\\times 0.9 = 2070W = 2.07kW$$

3. For AC Three-Phase Circuits:

$$P = \\\\sqrt{3} \\\\times U_{line} \\\\times I_{line} \\\\times \\\\cos\\\\varphi$$

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