Question

A certain resistance thermometer at triple point of water has resistance of 152.0 Ohms. What is the temperature of the system in Degrees Celsius when the resistance of the thermometer is 230.51 Ohms ?

(A) 414.2 Degrees Celsius

(B) 141.0 Degrees Celsius

(C) 253.2 Degrees Celsius

(D) 80.4 Degrees Celsius

Answer 1

The temperature at which the tungsten filament of a 12V and 36W lamp operates is 1730 Degrees Celsius. If the temperature coefficient of resistance of tungsten is $610^{\wedge} - 3 / K$, find the resistance of the lamp at a room temperature of 20 Degrees Celsius.

(A) 10.00 ohms

(B) 0.45 ohms

(C) 0.39 ohms

(D) 4.00 ohms

$$R_{1730} = R_{20} \left(1 + \alpha (T_{1730} - T_{20})\right) \rightarrow R_{20} = \frac{R_{1730}}{\left(1 + \alpha (T_{1730} - T_{20})\right)}$$ $$R_{1730} = \frac{U^{2}}{P}$$

Finally:

$$R_{20} = \frac{U^{2}}{P} \frac{1}{\left(1 + \alpha (T_{1730} - T_{20})\right)}$$ $$R_{20} = \frac{(12V)^{2}}{36W} \frac{1}{(1 + 6 * 10^{-3} 1 / K * 1710)} = 0.350 \, \text{hms}$$

Answer: $R_{20} = 0.350 \, \text{hms}$