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Resistivity vs Resistance Formula:
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The resistivity vs resistance formula relates the electrical resistance of a material to its intrinsic resistivity, length, and cross-sectional area. This fundamental relationship helps determine how much a material will resist the flow of electric current.
The calculator uses the resistivity formula:
Where:
Explanation: The formula shows that resistance is directly proportional to resistivity and length, but inversely proportional to cross-sectional area.
Details: Accurate resistance calculation is crucial for designing electrical circuits, selecting appropriate wire sizes, calculating power losses, and ensuring electrical safety in various applications.
Tips: Enter resistivity in Ω·m, length in meters, and cross-sectional area in square meters. All values must be positive numbers greater than zero.
Q1: What is the difference between resistivity and resistance?
A: Resistivity is an intrinsic property of a material, while resistance depends on both the material's resistivity and its physical dimensions (length and cross-sectional area).
Q2: What are typical resistivity values for common materials?
A: Copper: 1.68×10⁻⁸ Ω·m, Aluminum: 2.82×10⁻⁸ Ω·m, Silver: 1.59×10⁻⁸ Ω·m, Glass: 10¹⁰ to 10¹⁴ Ω·m.
Q3: How does temperature affect resistance?
A: For most conductors, resistance increases with temperature. The relationship is described by: R = R₀[1 + α(T - T₀)], where α is the temperature coefficient.
Q4: Why is cross-sectional area important?
A: Larger cross-sectional area provides more paths for electrons to flow, reducing resistance. This is why thicker wires have lower resistance.
Q5: What are the practical applications of this formula?
A: Used in electrical engineering for wire sizing, circuit design, heating element design, and calculating voltage drops in power transmission systems.