How Does Temperature Affect Electrical Resistance in Copper Wire?

In summary, the conversation is about solving a physics problem involving temperature, voltage, and current. The problem involves finding the current in a copper wire at a specific temperature in Antarctica, given the current at a different temperature in Death Valley. The student has attempted to solve the problem using an equation for resistance and temperature, but the equation is not accurate over such a wide temperature range. The correct approach is to use the definition of the temperature coefficient and integrate from a reference temperature, which in this case is 0°C.
  • #1
porporking
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0

Homework Statement


Hi Physicsforum, this is my first post so apology if I make unclear equation. I try to solve this question by pluging t0 as temp. at Valley and t as temp. at Antartitca directly as oppose to setting separate equation. I got different answer than the solution said

While taking photographs in Death Valley on a day
when the temperature is 58.0°C, Bill Hiker finds that
a certain voltage applied to a copper wire produces
a current of 1.00 A. Bill then travels to Antarctica
and applies the same voltage to the same wire. What
current does he register there if the temperature is
-88.0°C? Assume that no change occurs in the wire’s
shape and size.

The answer from solution book is 1.98 A

Homework Equations


ρ = [ρ0(1+α(T-T0))]

R = [R0(1+α(T-T0))]

The Attempt at a Solution


Rantart = [Rvalley(1+α(T-T0))]
V/Iantart = [V/Ivalley(1+α(T-T0))]

V are same so eliminate V on both side,

1/Iantart = [1/Ivalley(1+α(T-T0))]

Iantart = Ivalley/(1+α(T-T0))

substitute
Iantart= 1.00A/(1+(3.9*10^-3)(-88c-58c)) = 2.32 A
 
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  • #2
Over such a wide temperature range, the equation ρ = [ρ0(1+α(T-T0))] is not a good approximation.
Start with the definition α = (1/ρ)dρ/dT and integrate from T0 to T.
 
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  • #3
porporking said:

Homework Equations


ρ = [ρ0(1+α(T-T0))]

R = [R0(1+α(T-T0))]
The ##T_o## here is the reference temperature at which the value of ##\alpha## was determined. If you try to use some other temperature here (such as one of your sampled temperatures), then the equation will not describe the same line.

Luckily, the temperature coefficient you've quoted would appear to be the one for 0°C, so that your ##T_o## is actually zero.
 
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Related to How Does Temperature Affect Electrical Resistance in Copper Wire?

1. What is the relationship between resistance and temperature?

The resistance of a material increases as its temperature increases. This is because temperature causes the atoms in a material to vibrate more, which increases the collisions between electrons and atoms. These collisions impede the flow of electrons, resulting in higher resistance.

2. How does temperature affect the resistance of metals?

For most metals, an increase in temperature will lead to an increase in resistance. This is because metals have a positive temperature coefficient of resistance, meaning their resistance increases with temperature. However, some metals, such as tungsten, have a negative temperature coefficient of resistance, meaning their resistance decreases as temperature increases.

3. 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 usually expressed in parts per million per degree Celsius (ppm/°C). A positive TCR means the resistance increases with temperature, while a negative TCR means the resistance decreases with temperature.

4. How does temperature affect the resistance of semiconductors?

Unlike metals, semiconductors have a negative temperature coefficient of resistance, meaning their resistance decreases as temperature increases. This is because as temperature increases, more electrons are freed from their atoms and become available for conduction, resulting in a lower resistance.

5. What is the significance of the temperature coefficient of resistance in electronic devices?

The temperature coefficient of resistance is an important factor to consider in electronic device design. If a device operates at a wide range of temperatures, the TCR of its components can cause changes in resistance that affect the device's performance. This can lead to errors in measurements or malfunctions in the device. Therefore, engineers must carefully select materials with appropriate TCRs to ensure the reliability and accuracy of electronic devices.

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