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Resistance Formula:
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The conductivity to resistance formula calculates the electrical resistance of a material based on its conductivity, length, and cross-sectional area. This fundamental relationship in electrical engineering helps determine how easily electric current flows through a conductor.
The calculator uses the resistance formula:
Where:
Explanation: The formula shows that resistance is directly proportional to length and inversely proportional to both conductivity and cross-sectional area.
Details: Accurate resistance calculation is crucial for designing electrical circuits, selecting appropriate wire sizes, predicting power losses, and ensuring proper functioning of electrical systems.
Tips: Enter length in meters, conductivity in siemens per meter (S/m), and cross-sectional area in square meters (m²). All values must be positive and non-zero.
Q1: What is the relationship between conductivity and resistivity?
A: Conductivity (σ) is the reciprocal of resistivity (ρ). The formula can also be written as R = ρL/A, where ρ = 1/σ.
Q2: What are typical conductivity values for common materials?
A: Copper: ~5.96×10⁷ S/m, Aluminum: ~3.5×10⁷ S/m, Iron: ~1.0×10⁷ S/m, Silver: ~6.3×10⁷ S/m.
Q3: How does temperature affect conductivity and resistance?
A: For most metals, conductivity decreases (resistance increases) with rising temperature due to increased electron scattering.
Q4: What units should I use for cross-sectional area?
A: Use square meters (m²) for consistency. For wires, you may need to convert from diameter using A = πd²/4.
Q5: Can this formula be used for all materials?
A: This formula works well for homogeneous, isotropic materials with uniform cross-section. It may not be accurate for semiconductors or materials with non-linear behavior.