RMS Voltage using Area of X-Section(Single-Phase Two-Wire Mid-Point Earthed OS) Calculator

Formula Used:

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

Length of Overhead AC Wire (L):

Resistivity (ρ):

Ω·m

Power Transmitted (P):

Area of Overhead AC Wire (A):

m²

Line Losses (P_loss):

Phase Difference (Φ):

rad

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 mid-point earthed overhead system based on the cross-sectional area of the wire and other electrical parameters.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the RMS voltage by considering the electrical properties of the transmission line, including its length, resistivity, cross-sectional area, power losses, and phase characteristics.

3. Importance of RMS Voltage Calculation

Details: Accurate RMS voltage calculation is crucial for designing efficient power transmission systems, ensuring proper equipment sizing, and minimizing energy losses in overhead AC lines.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure all values are positive and valid (length > 0, resistivity > 0, power > 0, area > 0, losses > 0, phase ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is RMS voltage and why is it important?
A: RMS (Root Mean Square) voltage represents the equivalent DC voltage that would deliver the same power to a load. It's important because it provides a meaningful measure of AC voltage for power calculations.

Q2: How does wire cross-sectional area affect RMS voltage?
A: Larger cross-sectional area reduces resistance, which decreases voltage drop and losses, resulting in higher RMS voltage at the receiving end.

Q3: What is the significance of phase difference in this calculation?
A: Phase difference affects the power factor, which influences the real power delivery efficiency and consequently the voltage calculation.

Q4: When is this formula specifically applicable?
A: This formula is specifically designed for single-phase two-wire mid-point earthed overhead systems with distributed parameters.

Q5: What are typical resistivity values for overhead wires?
A: Copper: ~1.68×10⁻⁸ Ω·m, Aluminum: ~2.82×10⁻⁸ Ω·m, but actual values vary based on material purity and temperature.