Question

An aluminum wire has a resistance of 7.50Ω at 30.0∘C. Determine its resistance (in Ω ) at 430∘C. The temperature coefficient of resistivity for aluminum wire is 3.90×10−3(∘C)^−1.

Answer 1

To determine the resistance of an aluminum wire at 430°C, the formula incorporating the temperature coefficient of resistivity is used, applying the physical principle of resistance change with temperature in high school level physics.

Step-by-step explanation:

The subject of the question involves calculating the change in resistance of an aluminum wire due to temperature change using the temperature coefficient of resistivity. This relates to the concept of how resistance in materials changes with temperature, an important aspect in the field of physics, and is particularly relevant to high school level physics courses.

To calculate the new resistance at 430°C, we use the formula:
R = R0(1 + α(T - T0)),
where R is the resistance at the new temperature, R0 is the original resistance, α is the temperature coefficient of resistivity, and T is the new temperature while T0 is the original temperature.

By substituting the given values:
R = 7.50Ω(1 + 3.90×10−3°C⁻¹(430°C - 30.0°C)),
we can find the aluminum wire's resistance at 430°C.