RMS Voltage using Area of X-Section (1-Phase 2-Wire US) Calculator

Formula Used:

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

Length of Underground AC Wire (L):

Resistivity (ρ):

Ω·m

Power Transmitted (P):

Area of Underground AC Wire (A):

m²

Line Losses (P_loss):

Phase Difference (Φ):

Root Mean Square Voltage (V_rms):

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1. What is RMS Voltage using Area of X-Section?

The RMS Voltage using Area of X-Section formula calculates the root mean square voltage in a single-phase, two-wire underground AC system based on wire length, resistivity, transmitted power, cross-sectional area, line losses, and phase difference.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( V_{rms} \) — Root Mean Square Voltage (V)
\( L \) — Length of Underground AC Wire (m)
\( \rho \) — Resistivity (Ω·m)
\( P \) — Power Transmitted (W)
\( A \) — Area of Underground AC Wire (m²)
\( P_{loss} \) — Line Losses (W)
\( \Phi \) — Phase Difference (°)

Explanation: This formula calculates the RMS voltage by considering the electrical properties and physical characteristics of the underground AC wire system.

3. Importance of RMS Voltage Calculation

Details: Accurate RMS voltage calculation is crucial for designing efficient underground AC power distribution systems, ensuring proper voltage levels, and minimizing power losses.

4. Using the Calculator

Tips: Enter all required values with appropriate units. Ensure positive values for all parameters, with phase difference between 0-90 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is RMS voltage?
A: RMS (Root Mean Square) voltage is the equivalent DC voltage that would deliver the same power to a load as the AC voltage being measured.

Q2: Why is phase difference important in this calculation?
A: Phase difference affects the power factor, which influences the actual power delivered and the voltage requirements in AC systems.

Q3: How does wire area affect RMS voltage?
A: Larger wire cross-sectional area reduces resistance, which decreases voltage drop and line losses, potentially lowering the required RMS voltage.

Q4: What are typical resistivity values for underground wires?
A: Copper has resistivity of about 1.68×10⁻⁸ Ω·m, while aluminum has about 2.82×10⁻⁸ Ω·m at 20°C.

Q5: When should this calculation be used?
A: This calculation is essential for designing and analyzing single-phase, two-wire underground AC power distribution systems.