Question

To what temperature (in °C) must you raise a copper wire, originally at 20.0°C, to triple its resistance, neglecting any changes in dimensions?

Answer 1

Answer:

528.91°C

Explanation:

Neglecting any change in dimensions, the way that the resistance of a material changes after a variation in its temperature is given by the expression:

$R = R_o*(1+\alpha *(T_f-T_o))$

Where $R_o$ is the original resistance.

$\alpha$ is the temperature coefficient of the material, that relates the percentage that the resistance of the material will increase after a raise of 1°C in temperature. For copper, this value is equal to 0.00393/°C.

$T_f$ and $T_o$ is the final and original temperature, respectively.

$T_f = \frac{(\frac{R}{Ro}-1)}{\alpha}+T_o=\frac{3-1}{0.00393  oC^{-1}}+20.0 oC = 528.91oC$