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Resistance Formula:
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The resistance formula \( R = \rho \frac{L}{A} \) calculates the electrical resistance of a wire based on its material properties and physical dimensions. This fundamental equation in electrical engineering relates resistance to resistivity, length, and cross-sectional area.
The calculator uses the resistance formula:
Where:
Explanation: The resistance increases with length and resistivity, but decreases with increasing cross-sectional area. This relationship is fundamental to understanding conductor behavior in electrical circuits.
Details: Accurate resistance calculation is crucial for designing electrical circuits, selecting appropriate wire gauges, predicting voltage drops, and ensuring proper current flow in electrical systems.
Tips: Enter resistivity in Ω·m, length in meters, and cross-sectional area in m². All values must be positive numbers. Common resistivity values: copper = 1.68×10⁻⁸ Ω·m, aluminum = 2.82×10⁻⁸ Ω·m.
Q1: What Is Resistivity?
A: Resistivity is an intrinsic property of materials that quantifies how strongly they oppose electric current. It's measured in ohm-meters (Ω·m) and varies with temperature.
Q2: How Does Wire Thickness Affect Resistance?
A: Thicker wires (larger cross-sectional area) have lower resistance because there's more space for electrons to flow through, reducing collisions with atoms.
Q3: Why Does Resistance Increase With Length?
A: Longer wires provide more obstacles (atoms) for electrons to collide with, increasing the total resistance proportionally to the length.
Q4: What Are Typical Resistivity Values?
A: Conductors: copper (1.68×10⁻⁸), aluminum (2.82×10⁻⁸), silver (1.59×10⁻⁸) Ω·m. Insulators: glass (10¹⁰-10¹⁴), rubber (10¹³-10¹⁶) Ω·m.
Q5: How Does Temperature Affect Resistance?
A: For most conductors, resistance increases with temperature due to increased atomic vibrations that impede electron flow. The relationship is described by \( R = R_0[1 + \alpha(T - T_0)] \).