A platinum-resistance thermometer has a resistance of 10 \omega at 0^\circC and 18 \omega at 100^\circC. Assuming that resistance changes uniformly with temperature, what is the resistance of the thermometer when the temperature is 45^\circC?
A
27.8
B
17.8
C
13.6
D
6.4
E
3.6
Verified Correct Answer: C.
Physical Principles & Numerical Solution
18\omega ⇔ 100ºC
x ⇔ 45ºC
10\omega ⇔ 0ºC
\(\frac{ x - 10}{18 - 10} = \frac{ 45 - 0}{ 100 - 0}\)
100x - 1000 = 45 x 8
100x = 360 + 1000 = 1360
x = \(\frac{1360}{100}\) = 13.6.
Source: Myschool Past Questions Archive (Record #42898)