Length Using Area of X-Section (2-Wire Mid-Point Earthed DC US) Calculator

Formula Used:

\[ l = \frac{A \times P_{line} \times V_m^2}{2 \times P^2 \times \rho} \]

Area of Underground DC Wire (A):

m²

Line Losses (P_line):

Maximum Voltage (V_m):

Power Transmitted (P):

Resistivity (ρ):

Ω·m

Length of Wire DC (l):

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1. What is the Length Using Area of X-Section Formula?

The Length Using Area of X-Section formula calculates the length of a DC wire in a 2-wire mid-point earthed system based on the wire's cross-sectional area, line losses, maximum voltage, power transmitted, and material resistivity.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l = \frac{A \times P_{line} \times V_m^2}{2 \times P^2 \times \rho} \]

Where:

\( l \) — Length of Wire DC (meters)
\( A \) — Area of underground DC wire (m²)
\( P_{line} \) — Line losses (Watts)
\( V_m \) — Maximum voltage (Volts)
\( P \) — Power transmitted (Watts)
\( \rho \) — Resistivity (Ω·m)

Explanation: This formula calculates the maximum allowable wire length that maintains acceptable line losses for a given power transmission system.

3. Importance of Wire Length Calculation

Details: Accurate wire length calculation is crucial for designing efficient DC power transmission systems, minimizing energy losses, ensuring proper voltage levels, and optimizing system performance.

4. Using the Calculator

Tips: Enter all values in appropriate units (area in m², line losses in W, maximum voltage in V, power in W, resistivity in Ω·m). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why is wire length important in DC systems?
A: Wire length directly affects resistance and power losses in the system. Longer wires have higher resistance, leading to greater voltage drops and energy losses.

Q2: What factors affect the maximum allowable wire length?
A: The maximum length depends on wire material (resistivity), cross-sectional area, acceptable power loss, transmitted power, and system voltage.

Q3: How does wire area affect the calculation?
A: Larger cross-sectional areas reduce resistance, allowing for longer wire lengths while maintaining acceptable power losses.

Q4: What is typical resistivity for common wire materials?
A: Copper: ~1.68×10⁻⁸ Ω·m, Aluminum: ~2.82×10⁻⁸ Ω·m. Values may vary with temperature and purity.

Q5: When should this calculation be used?
A: This calculation is essential for designing DC power distribution systems, particularly in underground applications where mid-point earthing is used for safety and performance.