Answer :
The resistance of the wire at 150ºC is 39.2 Ω.
Given data
Length of the wire, l = 26 m
Diameter of the wire, d = 0.075 mm
Resistance of the wire, R1 = 51 ΩTemperature, T1 = 20 °C
We know that the resistance of a wire depends on its resistivity, length and cross-sectional area.
And, the resistivity of the wire's material can be calculated as follows:Resistivity formula
The resistance of a wire can be calculated by using the following formula:
Resistance formula Now, let's calculate the resistivity of the wire's material.
Resistivity calculation We know that the formula for resistance of a wire is given by;
Resistance formula Where l is the length of the wire, A is the cross-sectional area of the wire, ρ is the resistivity of the wire, and R is the resistance of the wire.
So, we can rewrite this equation as: Resistivity formula
Therefore, the resistivity of the wire's material is 1.58 x 10^-8 Ωm.Now, we have to calculate its resistance at 150ºC, in ohms, if the temperature coefficient of resistivity is the same as that of gold.
At 20ºC, the resistivity of gold is 2.44 x 10^-8 Ωm and its temperature coefficient of resistivity is 0.0034 K^-1.Using temperature coefficient of resistivity, we can find the resistivity of gold at 150ºC.
Resistivity of gold at 150ºCUsing the temperature coefficient of resistivity formula, we have:Temperature coefficient of resistivity formula
Substituting the given values, we get:So, the resistivity of gold at 150ºC is 2.44 x 10^-8 (1 + (0.0034 x (150 - 20))) = 2.44 x 10^-8 x 1.442 = 3.51 x 10^-8 Ωm.
Now, we can use the resistance formula to find the resistance of the wire at 150ºC.Resistance of the wire at 150ºCSubstituting the given values in the resistance formula, we get:
Therefore, the resistance of the wire at 150ºC is 39.2 Ω.
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