Calculate conductor resistance from resistivity, length, and area
Resistivity rho
Length L
Area A
Result
Answer
Step-by-Step Derivation
Wire Resistance Formula
R = rho L / A
R increases with length and decreases with area
Wire resistance depends on material resistivity, conductor length, and cross-sectional area. Keep units consistent so the final resistance is meaningful.
⚠Use consistent units. For example, rho in ohm mm^2/m, length in meters, and area in mm^2 gives resistance in ohms.
What Determines Wire Resistance?
A wire resists current because its material and geometry limit charge flow. Longer wires create more resistance, while thicker wires reduce resistance.
Resistivity
Material property that describes opposition to current.
Length Effect
Doubling length doubles resistance.
Area Effect
Doubling area halves resistance.
Practical Use
Wire resistance affects voltage drop and heating.
Example: With rho = 0.0175, L = 10 m, and A = 2.5 mm^2, R = 0.0175 x 10 / 2.5 = 0.07 ohm.
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