Area of X-Section using Resistance (3-Phase 4-Wire OS) Calculator

Formula Used:

\[ \text{Area of Overhead AC Wire} = \frac{\text{Resistivity} \times \text{Length of Overhead AC Wire}}{\text{Resistance Overhead AC}} \] \[ A = \frac{\rho \times L}{R} \]

Area of Overhead AC Wire (A):

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1. What is the Area of X-Section using Resistance Formula?

The Area of X-Section using Resistance formula calculates the cross-sectional area of an overhead AC wire based on its resistivity, length, and electrical resistance. This is particularly important in 3-phase 4-wire overhead systems for proper electrical design and efficiency.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ A = \frac{\rho \times L}{R} \]

Where:

\( A \) — Area of Overhead AC Wire (m²)
\( \rho \) — Resistivity of the material (Ω·m)
\( L \) — Length of Overhead AC Wire (m)
\( R \) — Resistance Overhead AC (Ω)

Explanation: The formula demonstrates the inverse relationship between cross-sectional area and electrical resistance - larger cross-sectional areas result in lower resistance for the same material and length.

3. Importance of Cross-Sectional Area Calculation

Details: Accurate calculation of cross-sectional area is crucial for determining current-carrying capacity, voltage drop, power loss, and overall efficiency in electrical power transmission systems.

4. Using the Calculator

Tips: Enter resistivity in Ω·m, length in meters, and resistance in ohms. All values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is resistivity and how does it affect the calculation?
A: Resistivity is a material property that measures how strongly a material opposes electric current. Different materials (copper, aluminum, etc.) have different resistivity values that significantly impact the area calculation.

Q2: Why is cross-sectional area important in overhead power lines?
A: Cross-sectional area determines the current-carrying capacity, mechanical strength, and electrical resistance of the conductor, affecting both safety and efficiency.

Q3: How does length affect the required cross-sectional area?
A: Longer conductors require larger cross-sectional areas to maintain the same resistance level, as resistance increases proportionally with length.

Q4: What are typical resistivity values for common conductor 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.

Q5: How does temperature affect this calculation?
A: Resistivity changes with temperature, so calculations should consider the operating temperature of the conductor for accurate results.