Question

At what temperature will aluminum have a resistivity that is three times the resistivity of tungsten at room temperature? (Assume room temperature is 20° C.)

Answer 1

Step-by-step explanation:

At room temperature, resistivity of tungsten is
`5.6 * 10^(-8)` and the resistivity of aluminium is
`2.8 * 10^(-8)`.

Temperature coefficient of aluminium (
`\alpha`) =
`3.9 * 10^(-3)`

`R_(a) = 3R_(c) = 5.1 * 10^(-8) \ohm m`

and,
`R_(a) = R_(o)(1 + \alpha * \Delta T)`

=
`2.82 * 10^(-8) (1 + 3.9 * 10^(-8) * \Delta T)`

`\Delta T = 207.3^(o)C`

T =
`(207.3 + 20)^(o)C`

=
`227.3^(o)C`

So, at
`227.3^(o)C` aluminium has resistivity which is three times the resistivity of tungsten at room temperature.