Length Of Wire Using Area Of X-Section(Single Phase Two Wire Mid-Point Earthed OS) Calculator

Formula Used:

\[ Length Of Overhead AC Wire = \frac{Area Of Overhead AC Wire \times Maximum Voltage Overhead AC^2 \times Line Losses \times \cos(Phase Difference)^2}{Resistivity \times Power Transmitted^2} \] \[ L = \frac{A \times V_m^2 \times P_{loss} \times \cos(\Phi)^2}{\rho \times P^2} \]

Area Of Overhead AC Wire:

m²

Maximum Voltage Overhead AC:

Line Losses:

Phase Difference:

rad

Resistivity:

Ω·m

Power Transmitted:

Length Of Overhead AC Wire:

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1. What Is The Length Of Wire Using Area Of X-Section Formula?

The Length Of Wire Using Area Of X-Section formula calculates the required length of overhead AC wire based on its cross-sectional area, maximum voltage, line losses, phase difference, resistivity, and transmitted power. This is essential for designing efficient single-phase two-wire mid-point earthed overhead systems.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ L = \frac{A \times V_m^2 \times P_{loss} \times \cos(\Phi)^2}{\rho \times P^2} \]

Where:

\( L \) — Length of Overhead AC Wire (m)
\( A \) — Area of Overhead AC Wire (m²)
\( V_m \) — Maximum Voltage Overhead AC (V)
\( P_{loss} \) — Line Losses (W)
\( \Phi \) — Phase Difference (rad)
\( \rho \) — Resistivity (Ω·m)
\( P \) — Power Transmitted (W)

Explanation: This formula accounts for electrical properties and losses to determine the optimal wire length for efficient power transmission.

3. Importance Of Wire Length Calculation

Details: Accurate wire length calculation is crucial for minimizing power losses, ensuring voltage stability, and optimizing the cost and efficiency of overhead power transmission systems.

4. Using The Calculator

Tips: Enter all values in appropriate units. Ensure positive values for area, voltage, losses, resistivity, and power. Phase difference should be in radians (0 to π/2 for typical systems).

5. Frequently Asked Questions (FAQ)

Q1: Why is wire length important in power transmission?
A: Wire length affects resistance, power losses, and voltage drop. Proper length calculation ensures efficient energy transfer and system stability.

Q2: What factors influence the optimal wire length?
A: Cross-sectional area, maximum voltage, allowable losses, phase difference, material resistivity, and transmitted power all influence the optimal wire length.

Q3: How does phase difference affect wire length calculation?
A: Phase difference affects the power factor, which influences the real power component and thus the calculation of required wire length.

Q4: Can this formula be used for DC systems?
A: This specific formula is designed for AC systems. DC systems would use a different calculation that doesn't account for phase difference.

Q5: What are typical resistivity values for common wire materials?
A: Copper: 1.68×10⁻⁸ Ω·m, Aluminum: 2.82×10⁻⁸ Ω·m, Silver: 1.59×10⁻⁸ Ω·m at 20°C.