RMS Voltage using Area of X-Section(Single Phase Two Wire OS) 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 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):

Unit Converter ▲

Unit Converter ▼

From:	To:

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

The RMS (Root Mean Square) Voltage using Area of X-Section formula calculates the effective voltage in a single-phase two-wire overhead system based on wire properties, power transmission, and losses.

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 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 physical properties of the wire, the power being transmitted, and the losses in the system.

3. Importance of RMS Voltage Calculation

Details: Accurate RMS voltage calculation is crucial for designing efficient power transmission systems, minimizing energy losses, and ensuring proper equipment operation.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure positive values for all parameters. Phase difference should be in radians (0 to π/2 for typical power factor angles).

5. Frequently Asked Questions (FAQ)

Q1: Why use RMS voltage instead of peak voltage?
A: RMS voltage represents the equivalent DC voltage that would deliver the same power to a load, making it more useful for power calculations.

Q2: What is the significance of wire area in this calculation?
A: Larger wire area reduces resistance, which decreases power losses and affects the required voltage for a given power transmission.

Q3: How does phase difference affect the RMS voltage?
A: Lower power factor (higher phase difference) requires higher voltage to transmit the same amount of real power, increasing system losses.

Q4: What are typical resistivity values for common conductor materials?
A: Copper: 1.68×10⁻⁸ Ω·m, Aluminum: 2.82×10⁻⁸ Ω·m, Silver: 1.59×10⁻⁸ Ω·m at 20°C.

Q5: When is this formula most applicable?
A: This formula is specifically designed for single-phase two-wire overhead AC transmission systems with known line losses.