A platinum resistance thermometer has a resistance of 10.59ohms at 0 degree celcius and 15.59ohms at 100 degree celcius. Assuming that the resistance changes uniformly with temperature, what is: (i) the temperature when the resistance is 10.59ohms? (ii) the resistance of the thermometer when the temperature is 55degree celcius?

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44.25 omhs

To answer these questions, we need to use the concept of linear interpolation. Linear interpolation is a method for estimating values that lie between two known data points by assuming a linear relationship between those points.

(i) To find the temperature when the resistance is 10.59 ohms, we can use the formula for linear interpolation:

temperature = temperature1 + (resistance - resistance1) × (temperature2 - temperature1) / (resistance2 - resistance1)

Given:
resistance1 = 10.59 ohms
temperature1 = 0 degrees Celsius
resistance2 = 15.59 ohms
temperature2 = 100 degrees Celsius
resistance = 10.59 ohms

Plugging in the values into the formula:

temperature = 0 + (10.59 - 10.59) × (100 - 0) / (15.59 - 10.59)
temperature = 0

Therefore, when the resistance is 10.59 ohms, the temperature is 0 degrees Celsius.

(ii) To find the resistance of the thermometer when the temperature is 55 degrees Celsius, we can use the same formula:

resistance = resistance1 + (temperature - temperature1) × (resistance2 - resistance1) / (temperature2 - temperature1)

Given:
resistance1 = 10.59 ohms
temperature1 = 0 degrees Celsius
temperature2 = 100 degrees Celsius
resistance2 = 15.59 ohms
temperature = 55 degrees Celsius

Plugging in the values into the formula:

resistance = 10.59 + (55 - 0) × (15.59 - 10.59) / (100 - 0)
resistance = 10.59 + (55 × 5) / 100
resistance = 10.59 + 2.775
resistance = 13.365 ohms

Therefore, when the temperature is 55 degrees Celsius, the resistance of the thermometer is approximately 13.365 ohms.