To determine the resistance of the platinum-resistance thermometer at 45 degrees Celsius, we can use the formula for resistance variation with temperature, which assumes a linear relationship between resistance and temperature.
The formula can be expressed as:
\[ R_t = R_0 + \left( \frac{R_{100} - R_0}{100} \right) \times t \]
Where:
- \(R_t\) is the resistance at temperature \(t\) in degrees Celsius.
- \(R_0\) is the resistance at 0 degrees Celsius (10 Ω).
- \(R_{100}\) is the resistance at 100 degrees Celsius (18 Ω).
- \(t\) is the temperature in degrees Celsius.
Given:
- \(R_0 = 10 , \Omega\)
- \(R_{100} = 18 , \Omega\)
- \(t = 45 , °C\)
Now, substituting the values into the formula:
- Calculate the change in resistance per degree:
\[ \frac{R_{100} - R_0}{100} = \frac{18 , \Omega - 10 , \Omega}{100} = \frac{8 , \Omega}{100} = 0.08 , \Omega/°C \]
- Now substitute this value back into the formula:
\[ R_t = R_0 + \left( \frac{R_{100} - R_0}{100} \right) \times t \]
\[ R_t = 10 , \Omega + (0.08 , \Omega/°C) \times 45 °C \]
\[ R_t = 10 , \Omega + 3.6 , \Omega = 13.6 , \Omega \]
Thus, the resistance of the thermometer at 45 degrees Celsius is:
\[ \boxed{13.6 , \Omega} \]
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