A platinum-resistance thermometer has a resistance of 5\Omega at 0^\circC and 9\Omega at l00^\circC. Assuming that resistance changes uniformly with temperature, calculate the resistance of the thermometer when the temperature is 45^\circC.
A
13.9 Ω
B
8.9 Ω
C
6.8 Ω
D
3.2 Ω
E
1.8 Ω
Verified Correct Answer: C.
Physical Principles & Numerical Solution
\(\frac{\theta}{100} = \frac{R_ {\theta} - R_0}{R_{100} - R_0}\)
\(\frac{45}{100} = \frac{R_{\theta} - 5}{9 - 5}\)
\(45 \times 4 = 100(R_{\theta} - 5)\)
\(180 = 100R_{\theta} - 500\)
\(180 + 500 = 100R_{\theta}\)
\(R_{\theta} = \frac{680}{100}\)
\(R_{\theta} = 6.8 \Omega\)
Source: Myschool Past Questions Archive (Record #25210)