Question

at what temperature will aluminium have a resistivity that is three times resistivity copper has at room temperature?

Answer 1

The temperature dependence of resistivity is given by equation

$$\rho(t)=\rho(20\degree {\rm C})(1+\alpha (t-20\degree \rm C)).$$

Rresistivity of metals at room temperature

$${\rho_{Cu}(20\degree {\rm C})=1.68\times 10^{-8}\rm \Omega\cdot m}\\ \rho_{Al}(20\degree {\rm C})=2.65\times 10^{-8}\rm \Omega\cdot m\\$$

Hence, we get equation

$$3\times1.68\times 10^{-8} =2.65\times 10^{-8}(1+0.00435 (t-20\degree \rm C)),$$ $${0.902 =0.00435 (t-20\degree \rm C)},\\ t=20+207=227\degree\rm C$$