The resistance of a platinum resistance thermometer is \(160.5 \Omega\) at steam point and \(60.5 \Omega\) at the melting point of Ice. Calculate the resistance of the thermometer at \(70^{\circ} C\)
A. \(160.5 \Omega\) B. \(165.5 \Omega\) C. \(130.5 \Omega\) D. \(170.5 \Omega\)
Correct Answer: C
Explanation
The problem is best handled using the method of interpolation which is shown below $$ \begin{array}{rl} 100^{\circ} C -160.5 \Omega \\ 70^{\circ} C - R _{\theta} \\ 0^{\circ} C & 60 \Omega \\ \frac{70-0}{100-0} & =\frac{R_{\theta}-60}{160.5-60} \\ \frac{70}{100} & =\frac{R_{\theta}-60}{100.5} \\ R_{\theta} & =\frac{70 \times 100.5}{100}+60 \\ & =130.5 \Omega \end{array} $$