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Question

The resistance of pure platinum increases linearly with temperature (over a small range). We can use this property to measure temperature of different bodies, relative to a scale.

If we scale the thermometer such that a resistance of 80 Ω denotes 0oC and 90 Ω denotes 100oC, what temperature will a resistance of 86 Ω denote?


A

400C

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B

500C

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C

600C

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D

800C

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Solution

The correct option is C

600C


A "linear” relation between two quantities, say, Q1 and Q2, means the following
Q1=mQ2+c

where m and c are constants. This follows from the fact that for a straight line on a plane, y and x are related as,
y=mx+c

m being the slope and c the y-intercept respectively.

In our case, this should be true between the temperature and the resistance at that temperature,
Rθ=αθ+β
for some constants α & β.
Let's find out what these constants are from the information given. We can write
80 Ω=α×0oC+β
β=80 Ω

90 Ω=α×100oC+β
α=9080100=0.1 Ω/oC

Using these values, the temperature(θ) can be written as
86=0.1×θ+80
θ=60oC



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