Factors Affecting Resistance
Resistance of a conductor depends on its length, cross-sectional area, and material: R = ρ L/A, where ρ is resistivity.
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Resistance and dimensions
For a uniform conductor, resistance R is directly proportional to length L and inversely proportional to cross-sectional area A: R = ρ L/A. The constant ρ (rho) is the resistivity of the material, in Ω·m. So longer or thinner wires have higher resistance.
Resistivity
Resistivity ρ depends on the material and temperature. Good conductors (copper, silver) have low ρ; insulators have very high ρ. Resistivity usually increases with temperature for metals.
Practical implications
Power lines use thick, low-resistivity conductors to minimise loss. Heating elements use materials with higher resistivity. Variable resistors (rheostats) change effective length or area to vary R.
Why do power lines use thick wires and not thin ones, even though both could carry the same current if the voltage were adjusted?