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Resistance Formula:
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The resistance formula \( R = \rho \times \frac{L}{A} \) calculates the electrical resistance of a material based on its resistivity (ρ), length (L), and cross-sectional area (A). This fundamental relationship helps determine how much a material opposes electric current flow.
The calculator uses the resistance formula:
Where:
Explanation: The resistance is directly proportional to both the resistivity of the material and its length, and inversely proportional to its cross-sectional area.
Details: Accurate resistance calculation is crucial for designing electrical circuits, selecting appropriate materials, and ensuring proper functioning of electrical systems. It helps prevent overheating and ensures efficient power transmission.
Tips: Enter resistivity in ohm-meters, length in meters, and cross-sectional area in square meters. All values must be positive numbers.
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).
Q2: How does length affect resistance?
A: Resistance increases with length - a longer conductor has more resistance than a shorter one of the same material and cross-section.
Q3: How does cross-sectional area affect resistance?
A: Resistance decreases as cross-sectional area increases - thicker wires have less resistance than thinner ones of the same material and length.
Q4: What are typical resistivity values?
A: Conductors like copper (1.68×10⁻⁸ Ω·m) have low resistivity, while insulators like rubber (10¹³ Ω·m) have very high resistivity.
Q5: Can this formula be used for any shape?
A: The formula works for uniform cross-sections. For complex shapes, integration may be needed to calculate total resistance.