Question

The resistance of a resistance thermometer have values $2.71$ and $3.70$ ohms at ${10}^{\circ }C$ and ${100}^{\circ }C$ respectively. The temperature at which the resistance is $3.26ohm$ is

• A. ${40}^{\circ }C$
• B. ${50}^{\circ }C$
• C. ${60}^{\circ }C$
• D. ${70}^{\circ }C$

Answer 1

Answer: (C)

${60}^{\circ }C$

We have,
$R_t=R_0(1+\alpha t)$
Here, $3.70=2.71[1+\alpha (100-10\left)\right]....\left(i\right)$
and $3.26=2.71[1+\alpha (x-10\left)\right]....\left(ii\right)$
From Eqs. (i) and (ii)
$\alpha =\frac{3.70-2.71}{90\times 2.71}=\frac{1}{90}\times 2.71...\left(iii\right)$
Substituting Eq. (iii) in Eq. (i)
$3.26=2.71[1+\frac{1}{9-\times 2.71}\times (x-10\left)\right]$
$=2.71+\frac{x-10}{90}$
or $\frac{x-10}{90}=3.26-2.71=0.55$
$\Rightarrow x=(90\times 0.55)+10$
$=49.5+10={59.5}^{\circ }C$
$={60}^{\circ }C$.