Resistivity Using Volume Of Conductor Material (3 Phase 3 Wire US) Calculator

Formula Used:

\[ \rho = \frac{V \times P_{\text{loss}} \times (V_m \times \cos(\Phi))^2}{7 \times (P \times L)^2} \]

Volume Of Conductor:

m³

Line Losses:

Maximum Voltage Underground AC:

Phase Difference:

rad

Power Transmitted:

Length of Underground AC Wire:

Resistivity:

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1. What is the Resistivity Calculation Formula?

The formula calculates the resistivity of conductor material in a 3-phase 3-wire underground AC system. Resistivity measures how strongly a material opposes the flow of electric current through it.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \rho = \frac{V \times P_{\text{loss}} \times (V_m \times \cos(\Phi))^2}{7 \times (P \times L)^2} \]

Where:

\( \rho \) — Resistivity (Ω·m)
\( V \) — Volume of conductor (m³)
\( P_{\text{loss}} \) — 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: The formula accounts for the relationship between conductor volume, power losses, voltage, phase difference, transmitted power, and wire length to determine material resistivity.

3. Importance of Resistivity Calculation

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

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why is resistivity important in power transmission?
A: Resistivity determines how much energy will be lost as heat during transmission. Lower resistivity materials result in more efficient power delivery.

Q2: What are typical resistivity values for common conductors?
A: Copper has resistivity of about 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.

Q3: How does temperature affect resistivity?
A: Resistivity generally increases with temperature for most conductors due to increased atomic vibrations that impede electron flow.

Q4: What factors can cause inaccurate resistivity calculations?
A: Temperature variations, material impurities, measurement errors in input parameters, and non-uniform conductor composition can affect accuracy.

Q5: How is this formula different from DC resistivity calculations?
A: This AC formula incorporates phase difference (cos Φ) and uses specific constants for 3-phase 3-wire underground systems, accounting for AC-specific effects.