Power Transmitted Using Constant(DC 3-Wire) Calculator

Power Transmitted Formula:

\[ P = V_m \times \sqrt{\frac{2 \times A \times K}{(2.5) \times (L^2) \times \rho}} \]

Maximum Voltage Overhead DC (V_m):

Volt

Area of Overhead DC Wire (A):

m²

Constant Overhead DC (K):

Length of Wire DC (L):

Resistivity (ρ):

Ω·m

Power Transmitted (P):

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1. What is the Power Transmitted Formula?

The Power Transmitted formula calculates the power transmitted through an overhead DC 3-wire system based on maximum voltage, wire area, system constant, wire length, and material resistivity. This formula provides an accurate assessment of power transmission capacity in DC systems.

2. How Does the Calculator Work?

The calculator uses the Power Transmitted formula:

\[ P = V_m \times \sqrt{\frac{2 \times A \times K}{(2.5) \times (L^2) \times \rho}} \]

Where:

\( P \) — Power Transmitted (Watt)
\( V_m \) — Maximum Voltage Overhead DC (Volt)
\( A \) — Area of Overhead DC Wire (m²)
\( K \) — Constant Overhead DC
\( L \) — Length of Wire DC (m)
\( \rho \) — Resistivity (Ω·m)

Explanation: The formula accounts for the relationship between voltage, wire characteristics, and material properties to determine the maximum power that can be transmitted through the DC system.

3. Importance of Power Transmission Calculation

Details: Accurate power transmission calculation is crucial for designing efficient DC power systems, determining system capacity, optimizing wire sizing, and ensuring reliable power delivery.

4. Using the Calculator

Tips: Enter maximum voltage in volts, wire area in square meters, system constant, wire length in meters, and resistivity in ohm-meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the constant K in the formula?
A: The constant K represents specific system characteristics and parameters that are unique to the overhead DC 3-wire configuration being analyzed.

Q2: How does wire length affect power transmission?
A: Longer wire lengths increase resistance and power loss, reducing the amount of power that can be effectively transmitted through the system.

Q3: Why is resistivity an important factor?
A: Resistivity determines how strongly the wire material opposes current flow, directly impacting power loss and transmission efficiency.

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: How accurate is this calculation for real-world applications?
A: This provides a theoretical maximum. Real-world systems may have additional factors like temperature variations, environmental conditions, and system losses that should be considered.