Active Power in Three Phase (L-L) AC Circuits Calculator

Active Power in Three Phase (L-L) AC Circuits Formula:

\[ P_{dc} = \sqrt{3} \times V_{line} \times I_{line} \times \cos(\theta_{ph}) \]

Active Power in DC Circuit (P_dc):

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1. What is Active Power in Three Phase (L-L) AC Circuits?

Active Power in Three Phase (L-L) AC Circuits represents the actual power consumed or utilized in the circuit to perform useful work. It is the real component of the apparent power in an AC system.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_{dc} = \sqrt{3} \times V_{line} \times I_{line} \times \cos(\theta_{ph}) \]

Where:

\( P_{dc} \) — Active Power in DC Circuit (Watt)
\( V_{line} \) — Line Voltage (Volt)
\( I_{line} \) — Line Current (Ampere)
\( \theta_{ph} \) — Phase Angle (Radian)
\( \sqrt{3} \) — Constant for three-phase systems
\( \cos \) — Cosine function

Explanation: The formula calculates the real power in a three-phase system by considering the line-to-line voltage, line current, and the cosine of the phase angle between them.

3. Importance of Active Power Calculation

Details: Accurate active power calculation is essential for power system analysis, energy billing, equipment sizing, and ensuring efficient operation of electrical systems.

4. Using the Calculator

Tips: Enter line voltage in volts, line current in amperes, and phase angle in radians. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why is √3 used in three-phase power calculations?
A: The √3 factor accounts for the phase difference between line-to-line and phase voltages in a balanced three-phase system.

Q2: What is the difference between active power and apparent power?
A: Active power is the real power consumed, while apparent power is the product of voltage and current without considering the phase angle.

Q3: How does phase angle affect active power?
A: The cosine of the phase angle (power factor) determines what portion of the apparent power is converted to useful work.

Q4: Can this formula be used for unbalanced three-phase systems?
A: This formula is specifically for balanced three-phase systems. Unbalanced systems require more complex calculations.

Q5: What are typical power factor values in electrical systems?
A: Power factor typically ranges from 0 to 1, with industrial systems often operating between 0.8-0.95. A power factor of 1 indicates purely resistive load.