Temperature Coefficient of Resistivity

In summary, the conversation discusses the equation R = R0[1+α(T-T0)] and the steps to solve for the temperature coefficient of resistivity. The correct steps involve isolating X by dividing 44.400 by 37.800 and then subtracting 1, resulting in X = .0402. However, the mistake in the conversation was adding 1 to 28.2 in the equation.
  • #1
Boozehound
29
0
A coil of wire has a resistance of 37.800 Ω at 27.800 °C and 44.400 Ω at 56.000 °C. What is the temperature coefficient of resistivity? Do not enter units.

Equation: R=R0[1+α(T-T0)]

then i plugged in number to make the equation look like this:

44.400=37.800[1+X(56.000-27.800)]

and i solve for X and i get X=.0402 and its wrong...

anyone see something i dont?
 
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  • #2
Can you show more of your steps to your final answer? You're making a mistake somewhere.
 
  • #3
44.400=37.800[1+X(56.000-27.800)

44.400=37.800[1+X(28.2)

44.400=37.800[1+28.2X]

44.400=37.800[29.2X]

1.1746=29.2X

.0402=X

those are the steps i used...im not too sure about what to do with the 1+X part but that might be where I am going wrong.
 
Last edited:
  • #4
Boozehound said:
44.400=37.800[1+X(56.000-27.800)

44.400=37.800[1+X(28.2)

44.400=37.800[1+28.2X]

44.400=37.800[29.2X]

1.1746=29.2X

.0402=X

those are the steps i used...im not too sure about what to do with the 1+X part but that might be where I am going wrong.

You can't add the 1 to the 28.2, since the units are not the same (it doesn't make sense to do that). You must go

(44.4/37.8) - 1 = 28.2X

in the next step to isolate X.
 
  • #5
ah! yeah now that you say it that doesn't make sense.. thank you very much!
 
  • #6
You're welcome. :smile:
 

1. What is the temperature coefficient of resistivity?

The temperature coefficient of resistivity is a measure of how much a material's resistance changes with a change in temperature. It is denoted by the symbol α and is expressed in units of inverse temperature (K-1 or °C-1).

2. How is the temperature coefficient of resistivity calculated?

The temperature coefficient of resistivity is calculated by taking the change in resistance (ΔR) divided by the original resistance (R) and the change in temperature (ΔT), and then multiplying it by the reciprocal of the original temperature (1/T). This is expressed as α = (ΔR/R)*(1/T)*(1/ΔT).

3. What is a positive and negative temperature coefficient of resistivity?

A positive temperature coefficient of resistivity means that as the temperature increases, the resistance of the material also increases. A negative temperature coefficient of resistivity means that as the temperature increases, the resistance of the material decreases.

4. How does the temperature coefficient of resistivity affect electrical circuits?

The temperature coefficient of resistivity plays an important role in electrical circuit design. It is necessary to consider the temperature coefficient of resistivity when selecting materials for use in electrical components and circuits in order to ensure the stability and accuracy of the system.

5. Can the temperature coefficient of resistivity be changed?

The temperature coefficient of resistivity is an intrinsic property of a material and cannot be changed. However, it can be compensated for by using materials with opposite temperature coefficients in a circuit, or by using a temperature compensation circuit that adjusts for any changes in resistance due to temperature.

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