Line Current Formula 3-Phase

Three-Phase Line Current Formula:

\[ I_{line} = \frac{P}{\sqrt{3} \times V_{line} \times PF} \]

Line Current (I_line):

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1. What is the Three-Phase Line Current Formula?

The three-phase line current formula calculates the current flowing through each line in a three-phase electrical system. It's essential for designing and analyzing balanced three-phase power systems commonly used in industrial and commercial applications.

2. How Does the Calculator Work?

The calculator uses the three-phase line current formula:

\[ I_{line} = \frac{P}{\sqrt{3} \times V_{line} \times PF} \]

Where:

\( I_{line} \) — Line current in amperes (A)
\( P \) — Total three-phase power in watts (W)
\( V_{line} \) — Line-to-line voltage in volts (V)
\( PF \) — Power factor (dimensionless, 0 to 1)
\( \sqrt{3} \) — Mathematical constant (approximately 1.732)

Explanation: This formula calculates the current per line in a balanced three-phase system, accounting for the phase relationship between voltage and current through the power factor.

3. Importance of Line Current Calculation

Details: Accurate line current calculation is crucial for proper sizing of circuit breakers, cables, transformers, and other electrical components in three-phase systems to ensure safety and efficiency.

4. Using the Calculator

Tips: Enter total three-phase power in watts, line-to-line voltage in volts, and power factor (between 0 and 1). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between line current and phase current?
A: In three-phase systems, line current is the current in each supply line, while phase current is the current through each load element. In star connection, they are equal; in delta connection, line current = √3 × phase current.

Q2: Why is √3 used in three-phase calculations?
A: √3 represents the relationship between line and phase quantities in three-phase systems. It accounts for the 120-degree phase displacement between phases.

Q3: What is power factor and why is it important?
A: Power factor is the ratio of real power to apparent power (0 to 1). It indicates how effectively electrical power is being used. Lower power factors result in higher currents for the same real power.

Q4: Can this formula be used for unbalanced systems?
A: This formula assumes a balanced three-phase system. For unbalanced systems, individual phase calculations are required.

Q5: What are typical power factor values?
A: Power factor typically ranges from 0.7 to 1.0. Industrial motors often operate around 0.8-0.9 PF, while purely resistive loads have PF = 1.0.