The resistance of a wire depends on both its material properties and its physical dimensions, as well as its temperature.
Resistance \( R \) can be described by the formula:
\[ R = \rho \frac{L}{A} \]
where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity of the material (which increases with temperature for conductors),
- \( L \) is the length of the wire,
- \( A \) is the cross-sectional area of the wire.
From the options given:
- A. thick wire and high temperature: A thick wire has a lower resistance due to a larger cross-sectional area, but high temperature increases resistivity.
- B. thin wire and high temperature: A thin wire has a higher resistance to begin with, and high temperature further increases resistivity.
- C. thick wire and cold temperature: A thick wire has a lower resistance due to its larger cross-sectional area, and cold temperature decreases resistivity.
- D. thin wire and low temperature: Although the temperature is low (which reduces resistivity), a thin wire still has a higher resistance due to a smaller cross-sectional area.
The lowest resistance will occur in C. thick wire and cold temperature, because the combination of lower resistivity at cold temperatures and a larger cross-sectional area from the thick wire results in the lowest overall resistance.
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