Question

Resistance of a platinum resistance thermom-eter is 2 ohm at ${20}^{\circ }C$, 4ohm at ${100}^{\circ }C$ and 2.2 ohm at some temperature. this temperature-is

• A. ${20}^{\circ }C$
• B. ${30}^{\circ }$
• C. ${40}^{\circ }C$
• D. ${28}^{\circ }C$

Answer 1

The correct option is D ${28}^{\circ }C$

Given,

Resistance at $20{}^{o}C$ is $2\Omega$

Resistance at ${100}^{o}C$ is $4\Omega$

Resistance of wire and temperature relation, $R=R_o(1+\alpha \Delta T)$

Coefficient of thermal expansion, $\alpha =\frac{R-R_o}{R_o\Delta T}=\frac{4-2}{2\times (100-20)}=0.0125$

At resistance, $2.2\Omega$

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

$2.2=2[1+0.0125(T-20)]$

$T=28{}^{o}C$

Hence, temperature is $28{}^{o}C$