Length of Wire using K(Two-Wire One Conductor Earthed) Calculator

Formula Used:

\[ Length of Wire DC = \sqrt{\frac{Constant Overhead DC \times Line Losses \times (Maximum Voltage Overhead DC^2)}{4 \times Resistivity \times (Power Transmitted^2)}} \] \[ L = \sqrt{\frac{K \times P_{loss} \times (V_m^2)}{4 \times \rho \times (P^2)}} \]

Constant Overhead DC (K):

Line Losses (P_loss):

Watt

Maximum Voltage Overhead DC (V_m):

Volt

Resistivity (ρ):

Ω·m

Power Transmitted (P):

Watt

Length of Wire DC (L):

Meter

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1. What is the Length of Wire using K Formula?

The Length of Wire using K formula calculates the required length of a DC overhead wire in a two-wire one conductor earthed system based on system constants, losses, voltage, resistivity, and power transmission requirements.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L = \sqrt{\frac{K \times P_{loss} \times (V_m^2)}{4 \times \rho \times (P^2)}} \]

Where:

\( L \) — Length of Wire DC (meters)
\( K \) — Constant Overhead DC
\( P_{loss} \) — Line Losses (Watt)
\( V_m \) — Maximum Voltage Overhead DC (Volt)
\( \rho \) — Resistivity (Ω·m)
\( P \) — Power Transmitted (Watt)

Explanation: This formula calculates the optimal wire length that balances system losses, voltage requirements, and power transmission efficiency.

3. Importance of Wire Length Calculation

Details: Accurate wire length calculation is crucial for efficient power transmission, minimizing energy losses, maintaining voltage stability, and ensuring proper system design in overhead DC transmission systems.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure all values are positive and within reasonable ranges for accurate calculations.

5. Frequently Asked Questions (FAQ)

Q1: What is Constant Overhead DC (K)?
A: Constant Overhead DC is a system-specific constant that accounts for various factors including conductor configuration and system geometry.

Q2: How does resistivity affect wire length?
A: Higher resistivity materials require shorter wire lengths to maintain the same power transmission efficiency and minimize losses.

Q3: What are typical resistivity values for common conductors?
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.

Q4: How does voltage affect the required wire length?
A: Higher transmission voltages allow for longer wire lengths while maintaining acceptable power losses due to reduced current requirements.

Q5: When should this calculation be used?
A: This calculation is essential for designing efficient overhead DC transmission systems, particularly in two-wire one conductor earthed configurations.