• question_answer 48) The resistance of a resistance thermometel have values 2.71 and 3.70 ohms at $10{{\,}^{o}}C$and $100{{\,}^{o}}C$respectively. The temperature at which the resistance is 3.26 ohm is A) $40{{\,}^{o}}C$               B) $50{{\,}^{o}}C$ C)  $60{{\,}^{o}}C$               D) $7\,0{{\,}^{o}}C$

We have, ${{R}_{t}}={{R}_{0}}(1+\alpha t)$ Here,    $3.70=2.71[1+\alpha (100-10)]$?(i) and $3.26=2.71[1+\alpha (x-10)]$ ?(ii) From Eqs. (i) and (ii) $\alpha =\frac{3.70-2.71}{90\times 2.71}=\frac{1}{90}\times 2.71$ ?(iii) Substituting Eq. (iii) in Eq. (i)    . $3.26=2.71\left[ 1+\frac{1}{90\times 2.71}\times (x-10) \right]$ $=2.71+\frac{x-10}{90}$ or $\frac{x-10}{90}=3.26-2.71=0.55$ $\Rightarrow$ $x=(90\times 0.55)+10$ $=49.5+10$ $=59.5{{\,}^{o}}C$ $=60{{\,}^{o}}C$