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

Formula Used:

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

Power Transmitted (P):

Watt

Phase Difference (Φ):

Radian

Resistivity (ρ):

Ω·m

Length of Underground AC Wire (L):

Meter

Area of Underground AC Wire (A):

m²

Line Losses (P_loss):

Watt

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 1-phase 2-wire mid-point earthed system based on power transmitted, phase difference, resistivity, wire length, cross-sectional area, and line losses.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the RMS voltage by considering the power factor, material properties, and system dimensions to determine the effective voltage in the system.

3. Importance of RMS Voltage Calculation

Details: Accurate RMS voltage calculation is crucial for proper system design, ensuring efficient power transmission, minimizing losses, and maintaining equipment safety in underground AC systems.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure positive values for all parameters. The phase difference should be in radians (0 to 2π range).

5. Frequently Asked Questions (FAQ)

Q1: Why is RMS voltage important in AC systems?
A: RMS voltage represents the equivalent DC voltage that would deliver the same power to a load, making it the standard measurement for AC systems.

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

Q3: What is the significance of phase difference in this calculation?
A: Phase difference affects the power factor (cosΦ), which determines the ratio of real power to apparent power in the system.

Q4: How do line losses impact the RMS voltage?
A: Higher line losses indicate more power dissipation as heat, resulting in greater voltage drop along the transmission line.

Q5: Can this formula be used for overhead transmission lines?
A: While the basic principles are similar, overhead lines have different characteristics and may require adjustments for accurate calculations.