A platinum-resistance thermometer has a resistance of 5Ω at 0°C and 9Ω at l00°C. Assuming that resistance changes uniformly with temperature, calculate the resistance of the thermometer when the temperature is 45°C.

  • A 13.9 Ω
  • B 8.9 Ω
  • C 6.8 Ω
  • D 3.2 Ω
  • E 1.8 Ω
waec 1996physics

The correct answer is C. 6.8 Ω

\(\frac{\theta}{100} = \frac{R_ {\theta} - R_0}{R_{100} - R_0}\)

\(\frac{45}{100} = \frac{R_{\theta} - 5}{9 - 5}\)

\(45 \times 4 = 100(R_{\theta} - 5)\)

\(180 = 100R_{\theta} - 500\)

\(180 + 500 = 100R_{\theta}\)

\(R_{\theta} = \frac{680}{100}\)

\(R_{\theta} = 6.8 \Omega\)

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