Resistance of a platinum wire is 2ohm at 0^c and 2.5ohm at 100^c then what temp its resistance wouldbe 2.3ohm
Answers
Concept:
Relation between the coefficient of thermal expansion and resistance is given by the formula- α = R - R₀/R₀ΔT
Given:
Resistance of platinum wire at 0⁰C is 2ohm
Resistance of platinum wire at 100⁰C is 2.5 ohm
Find:
We need to determine the temperature of the platinum wire at a resistance of 2.3ohm.
Solution:
Resistance of wire and temperature is related by an equation- R = R₀(1+αΔT) where α = coefficient of thermal expansion
The coefficient of thermal expansion, α explains how an object's size varies when temperature changes.
It is mathematically represented as- α = R - R₀/R₀ΔT
α = 2.5 - 2/ 2(100-0)
α = 0.0025
Therefore, at resistance 2.3 ohm
R = R₀(1+αΔT)
2.3 = 2[1 + 0.0025(T - 0)]
2.3 = 2 + 0.005T
T = 2.3 -2 / 0.005
T = 60⁰C
Thus, the temperature of the 2.3 ohm resistance is 60⁰C.
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