Temperature coefficient of resistance problem

In summary, the conversation involves finding the resistance at 20°C and the temperature coefficient of resistance alpha using a given graph. The formula R(T) = R(To) ( 1 + alpha (T-To) ) is suggested, but the individual feels uncertain due to limited data. Another formula, α = (R2 - R1)/(R1t2 - R2t1), is proposed and the values of R1 and R2 from the graph are used to find the alpha value. The individual also suggests interpolating the graph to find the resistance at 0°C and then using the formula to find the resistance at 20°C.
  • #1
sphys4
21
0

Homework Statement


For the resistance versus temperature graph below, find (a) the resistance at T = 20°C and (b) the temperature coefficient of resistance alpha .

http://tinypic.com/r/jhufkn/7

I don't know if the graph is showing up or not, it isn't for me... so here's the link.
http://tinypic.com/r/jhufkn/7

The Attempt at a Solution



I believe that this is the formula i am supposed to use, but i feel like i don't have enough numbers or data to plug in. R(T) = R(To) ( 1 + alpha (T-To) )
 
Last edited:
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  • #2
You can use the formula
α = (R2 - R1)/(R1t2 - R2t1)
From the graph, you can see that at 20 degree C R1 = 5.1 ohm and at 30 degree C R2 = 5.2 ohm. find α.
Interpolate the graph towards the axis. You can find R(0). Then use the formula which you have mentioned to find R(20)
 

FAQ: Temperature coefficient of resistance problem

What is the temperature coefficient of resistance?

The temperature coefficient of resistance (TCR) is a measure of how much the resistance of a material changes with temperature. It is typically expressed as a percentage change in resistance per degree Celsius.

Why is the temperature coefficient of resistance important?

The TCR is important because it helps us understand how the resistance of a material will change with temperature. This is crucial in many practical applications, such as designing electronic circuits or selecting materials for use in high temperature environments.

How is the temperature coefficient of resistance calculated?

The TCR is calculated by taking the change in resistance (in ohms) and dividing it by the change in temperature (in degrees Celsius). This can be expressed as a formula: TCR = (R2 - R1) / (R1 * (T2 - T1)), where R is the resistance and T is the temperature.

What factors affect the temperature coefficient of resistance?

The TCR of a material can be affected by several factors, including the type of material, its composition, and its physical and chemical properties. Generally, metals have a positive TCR, meaning their resistance increases with temperature, while semiconductors have a negative TCR, meaning their resistance decreases with temperature.

How can the temperature coefficient of resistance be used to predict the behavior of a material?

Knowing the TCR of a material can help predict how its resistance will change with temperature. This information is useful in practical applications, such as designing temperature sensors or determining the operating range of electronic devices. Additionally, the TCR can also be used to identify and characterize unknown materials.

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