How current changes in metals at different temperatures

[ketchuppy]

Homework Statement

While taking photographs in Death Valley on a day when the temperature is 59.0°C, Bill Hiker finds that a certain voltage applied to a aluminum wire produces a current of 1.000 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.

Homework Equations

I need to find the new current at a different temperature

The Attempt at a Solution

I used the equation Rf = Ri [1+alpha(Tf-Ti)

And was thinking that i would find Rf and then use ohm's law to find I for the final temperature. but i don't know what V is. or maybe i have to solve using another equation and then subtituing it in.

 

[Hootenanny]

Homework Statement

While taking photographs in Death Valley on a day when the temperature is 59.0°C, Bill Hiker finds that a certain voltage applied to a aluminum wire produces a current of 1.000 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.

Homework Equations

I need to find the new current at a different temperature

The Attempt at a Solution

I used the equation Rf = Ri [1+alpha(Tf-Ti)

And was thinking that i would find Rf and then use ohm's law to find I for the final temperature. but i don't know what V is. or maybe i have to solve using another equation and then subtituing it in.

Welcome to PF ketchuppy,

Indeed, you do not know the value of the voltage applied explicitly, but you do know that the voltage applied in both cases was the same.

 

[ketchuppy]

Indeed, you do not know the value of the voltage applied explicitly, but you do know that the voltage applied in both cases was the same.

yes that was stated in the problem . I was thinking that this relates to the resistivity since that changes with temperature. There an equation that relates Resistance to resitivity.

R = Resistivity (L/A).

Not sure if i could go anywhere with that

 

[Hootenanny]

yes that was stated in the problem . I was thinking that this relates to the resistivity since that changes with temperature. There an equation that relates Resistance to resitivity.

R = Resistivity (L/A).

Not sure if i could go anywhere with that

Let's go back to the original problem. Write out the two equations for resistance, one for each location.

 

[ketchuppy]

Let's go back to the original problem. Write out the two equations for resistance, one for each location.

I'm not sure which equation for resistance to use

 

[Hootenanny]

I'm not sure which equation for resistance to use

The one you stated in your opening post:

I used the equation Rf = Ri [1+alpha(Tf-Ti)

But perhaps it would be more useful in this case to use Ohm's law and re-write it as:

$$\frac{V}{I_f} = \frac{V}{I_i}\left[1+\alpha\left(T_f-T_i\right)\right]$$

 

[ketchuppy]

But perhaps it would be more useful in this case to use Ohm's law and re-write it as:

$$\frac{V}{I_f} = \frac{V}{I_i}\left[1+\alpha\left(T_f-T_i\right)\right]$$

since the voltage is the same, they would drop out of the equation

 

[Hootenanny]

since the voltage is the same, they would drop out of the equation

Indeed they would.

 

[ketchuppy]

would i then proceed to plug in the variables and solve for I(f)

 

[Hootenanny]

would i then proceed to plug in the variables and solve for I(f)

Sounds like a plan to me.

 

[berkeman]

One caveat -- I think the temperatures T need to be in absolute units (Kelvins), not C or F...