Resistivity using Area of X-Section (1-Phase 2-Wire Mid-Point Earthed) Calculator

Resistivity Formula:

\[ \rho = \frac{A \times P_{loss} \times (V_m \times \cos(\Phi))^2}{4 \times P^2 \times L} \]

Area of Underground AC Wire (A):

m²

Line Losses (P_loss):

Maximum Voltage Underground AC (V_m):

Phase Difference (Φ):

rad

Power Transmitted (P):

Length of Underground AC Wire (L):

Resistivity (ρ):

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1. What is Resistivity?

Resistivity is the measure of how strongly a material opposes the flow of current through them. It's a fundamental property that determines how well a material conducts electricity.

2. How Does the Calculator Work?

The calculator uses the resistivity formula:

\[ \rho = \frac{A \times P_{loss} \times (V_m \times \cos(\Phi))^2}{4 \times P^2 \times L} \]

Where:

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

Explanation: This formula calculates the resistivity of the wire material based on electrical parameters and physical dimensions of the underground AC system.

3. Importance of Resistivity Calculation

Details: Accurate resistivity calculation is crucial for designing efficient electrical systems, selecting appropriate wire materials, and minimizing power losses in underground AC transmission.

4. Using the Calculator

Tips: Enter all values in appropriate units. Area in square meters, losses and power in watts, voltage in volts, phase difference in radians, and length in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical resistivity range for common conductors?
A: Copper has resistivity around 1.68×10⁻⁸ Ω·m, aluminum about 2.82×10⁻⁸ Ω·m, and silver about 1.59×10⁻⁸ Ω·m at 20°C.

Q2: How does temperature affect resistivity?
A: Resistivity generally increases with temperature for most conductors due to increased atomic vibrations that impede electron flow.

Q3: Why is phase difference important in this calculation?
A: Phase difference affects the power factor, which influences the actual power delivered and the voltage-current relationship in AC systems.

Q4: What are common causes of line losses?
A: Line losses primarily occur due to resistance in conductors (I²R losses), but also include dielectric losses, radiation losses, and corona losses.

Q5: How accurate is this calculation for real-world applications?
A: This provides a theoretical calculation. Real-world applications should consider temperature variations, skin effect, proximity effect, and other practical factors.