Length Using Resistance of Natural Wire (2-Phase 3-Wire US) Calculator

Formula Used:

\[ Length\ of\ Underground\ AC\ Wire = \frac{Resistance\ Underground\ AC \times \sqrt{2} \times Area\ of\ Underground\ AC\ Wire}{Resistivity} \] \[ L = \frac{R \times \sqrt{2} \times A}{\rho} \]

Length of Underground AC Wire (L):

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1. What is the Length Using Resistance of Natural Wire Formula?

The Length Using Resistance of Natural Wire formula calculates the length of an underground AC wire in a 2-Phase 3-Wire US system based on its resistance, cross-sectional area, and material resistivity. This calculation is essential for proper electrical system design and analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Length\ of\ Underground\ AC\ Wire = \frac{Resistance\ Underground\ AC \times \sqrt{2} \times Area\ of\ Underground\ AC\ Wire}{Resistivity} \] \[ L = \frac{R \times \sqrt{2} \times A}{\rho} \]

Where:

\( L \) — Length of Underground AC Wire (meters)
\( R \) — Resistance Underground AC (ohms)
\( A \) — Area of Underground AC Wire (square meters)
\( \rho \) — Resistivity (ohm-meters)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: The formula accounts for the relationship between resistance, material properties, and physical dimensions of the wire in a 2-phase 3-wire underground AC system.

3. Importance of Length Calculation

Details: Accurate length calculation is crucial for proper voltage drop analysis, power loss estimation, and ensuring the electrical system meets performance requirements in underground AC installations.

4. Using the Calculator

Tips: Enter resistance in ohms, area in square meters, and resistivity in ohm-meters. All values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why is the √2 factor included in the formula?
A: The √2 factor accounts for the phase relationship in 2-phase 3-wire AC systems, where the voltage and current relationships differ from single-phase systems.

Q2: What are typical resistivity values for common conductor materials?
A: Copper: ~1.68×10⁻⁸ Ω·m, Aluminum: ~2.82×10⁻⁸ Ω·m. Actual values may vary based on material purity and temperature.

Q3: How does temperature affect the calculation?
A: Resistivity changes with temperature. For accurate results, use resistivity values at the expected operating temperature or apply appropriate temperature correction factors.

Q4: Can this formula be used for overhead lines?
A: While the basic principles are similar, overhead lines may have different considerations such as sag, tension, and environmental factors that aren't accounted for in this specific formula.

Q5: What are the limitations of this calculation?
A: This calculation assumes uniform material properties, constant cross-section, and doesn't account for skin effect, proximity effect, or frequency-dependent losses that may occur in AC systems.