Question

At what temperature would the resistance of a copper conductor be double its resistance at $0^o$C? Given $\alpha$ for copper is $3.9\times {10}^{-3}$ ${}^o{C}^{-1}$.

• A. ${256.4}^o$C
• B. ${512.8}^o$C
• C. ${100}^o$C
• D. $256.4$K

Answer 1

Answer: (A)

${256.4}^o$C

Given:

$R=2R_o$

$\alpha =3.9\times {10}^{-3}{C}^{-1}$

$\Delta T=T-T_o$

$R_o$ and $T_o$ are resistance and temperature at $0^{\circ }C$

$R$ and $T$ are resistance and temperature at $T^{\circ }C$

$R=R_o(1+\alpha \Delta T)$

Substituting the given information,

$2R_o=R_o(1+\alpha \Delta T)$

$2=1+\alpha \Delta T$

$1=\alpha \Delta T$

$1=3.9\times {10}^{-3}\Delta T$

$\Delta T={256.41}^{\circ }C$

$T-T_o=T-0=T={256.41}^{\circ }C$

Hence the correct option is (A).