Resistance vs. Temperature, etc.

In summary: Try it this waySolving for V in the same equation:Q=P\times VorP=Q\times VWith those two values, you can easily find how long you could surf the internet with the same amount of energy used in baking the cake.
  • #1
kkurutz
5
0
Hi, I have two homework questions that I'm stuck on. I've worked my way through both of them, but and coming up w/ the wrong answers. Here they are:

1) A copper wire has a resistance of 0.501 ohms at 20.0 degrees C, and an iron wire has a resistance of 0.486 ohms at the same temperature. At what temperature are their resistances equal?

First, I found the resistivities of each of the materials and filled in the following equation for each, then setting them eqaul: R = R(1 + alpha(T-T(ini.))

I then set the equality equal to zero: 0 = (R(copper) - R(iron)) + ([R(copper)*alpha(copper)] - [R(iron)*alpha(iron)]) * (T - T(ini.))

I then solved for T: T = T(ini.) + ( R(copper) - R(iron) ) \ ( [R(copper)*alpha(copper)] - [R(iron)*alpha(iron)])

After plugging in all the values, I'm coming up w/ -11.2 degree C though this is the wrong answer


2) In baking a cake, an electric oven uses an average of 19 A of electricity at 230 V for 45 minutes. A personal computer uses only 1.5 A at 115 V. With the same amount of electrical energy used in baking the cake, how long could you surf the internet on the computer?


Starting out, I found the power of the oven: P = IV

I then plugged to the power and other known values into the equation: P = (Q \ t)V to find the energy.

Then, I found the power of the computer: again, P = IV

Lastly, I plugged in the known values (P, Q, V) into: P = (Q \ t)V

I'm coming up w/ 570 minutes, which is the wrong answer.




If anyone can help me out and let me know what I'm doing wrong, I'd greatly appreciate it ... thanks in adavance.

-Keith
 
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  • #2
2) The amount of electrical energy used in both processes are the same which can be calculated from
[tex]I_1V_1\Delta t_1=I_2V_2\Delta t_2[/tex]
the time shoud be in seconds for S.I. units, but factor 60 appears both sides, so you can drop it and work in minutes. I got 19 hours.
 
  • #3
Thanks a lot for your help andrevhd. Anyone have any ideas for the first problem?
 
  • #4
1)Try it this way with symbols first
[tex]R_{copper}=R_{iron}[/tex]
so we are going to have all copper quantities on the lhs and iron on the rhs
[tex]R_c(1+{\alpha}_c\Delta T)=R_i(1+{\alpha}_i\Delta T)[/tex]
next the ratio
[tex]a=\frac{R_c}{R_i}[/tex]
changing the above to
[tex]a+a{\alpha}_c\Delta T=1+{\alpha}_i\Delta T[/tex]
...
 
  • #5
So am I solving for T in the following equation then: [tex]a+a{\alpha}_c\Delta T=1+{\alpha}_i\Delta T[/tex]

I tried doing that, but apparently my algebra sucks and I didn't rearrange the equation correctly. Sometimes I think math is my biggest problem w/ this class.
 
  • #6
[tex]\Delta T=T-T_{ini}[/tex]
so you want
[tex]\Delta T[/tex]
on the lhs of the equation, hopefully all the quantities on the rhs are known at that stage.
 

1. What is the relationship between resistance and temperature?

The relationship between resistance and temperature is an inverse one. This means that as temperature increases, resistance decreases and vice versa. This can be explained by the fact that as temperature increases, the atoms in a material vibrate more, causing more collisions and hindering the flow of electrons, thus increasing resistance.

2. How does temperature affect the resistance of conductors and insulators differently?

Temperature affects the resistance of conductors and insulators differently due to the difference in their atomic structures. In conductors, the atoms are closely packed, allowing for more collisions and thus an increase in resistance with temperature. In insulators, the atoms are more spread out, and the increase in temperature causes them to vibrate more, increasing the space between them and allowing for easier flow of electrons, resulting in a decrease in resistance.

3. What is the temperature coefficient of resistance?

The temperature coefficient of resistance is a measure of how much the resistance of a material changes with temperature. It is represented by the symbol α and is usually expressed in parts per million (ppm) per degree Celsius. It is a characteristic of each material and is used to calculate the change in resistance for a given change in temperature.

4. How is resistance vs. temperature graphically represented?

The relationship between resistance and temperature is usually graphically represented by plotting resistance on the y-axis and temperature on the x-axis. The resulting graph is typically a curved line, with resistance decreasing as temperature increases. The slope of this curve is determined by the material's temperature coefficient of resistance.

5. What are some practical applications of the relationship between resistance and temperature?

The relationship between resistance and temperature has several practical applications. One example is in thermistors, which are devices that use the change in resistance with temperature to measure and control temperature. It is also essential in the design and functioning of electronic circuits, where changes in temperature can affect the performance of components. Additionally, this relationship is crucial in understanding the behavior of materials in extreme temperatures, such as in aerospace or industrial applications.

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