Question

What is the effect of temperature on the resistance of a metal? The resistance of a platinum resistances thermometer at $0^o$C temperature is $3.0\Omega$ and at ${100}^o$C it is $3.75\Omega$. Its resistance at an unknown temperature is $3.15\Omega$. Find the value of the unknown temperature.

Answer 1

Resistance of metal (or conductor) increases with increases in temperature and vice-versa.
Given : $R_o=3\Omega$ at $T_o=0^{o}C$
Also, restsiance at $T_1={100}^{o}C$ is $R_1=3.75\Omega$
Using $R_1=R_o(1+\alpha \Delta T)$
Here, $\Delta T=T_1-T_o=100-0={100}^{o}C$
Or $3.75=3(1+\alpha \times 100)$
$⟹\alpha =2.5\times {10}^{-3}{/}^{o}C$
GIven : $R_2=3.15\Omega$
Using $R_2=R_o(1+\alpha \Delta T)$
Here, $\Delta T=T_2-T_o=T_2-0=T_2$
Or $3.15=3(1+2.5\times {10}^{-3}{T}_2)$
Or $2.5\times {10}^{-3}{T}_2=0.05$
$⟹T_2={20}^{o}C$