Resistance problem (Simple electrical problem)

In summary, the conversation is about determining the resistance of a copper wire at 80°C given its resistance at 10°C and the temperature coefficient at 0°C. The solution involves using the equation R2 = R1(1+\alpha1*ΔT) and assuming that the temperature coefficient remains constant within a certain temperature range. The final solution is to find R80 using the equation R80= R0 (1+0.00393*(80-0)).
  • #1
Rito3d03
4
0

Homework Statement


This question comes from one of my previous exam
and I still couldn't solve it after days of trying
hope someone can guide me through this thanks

A copper wire has a resistance of 10Ω at 10°C.
Determine the resistance of the wire at 80°C.
Given that the temperature coefficient of the wire is 0.00393C-1 at 0°C.

Homework Equations


R2 = R1(1+[itex]\alpha[/itex]1*ΔT)

The Attempt at a Solution


I don't know where to start when I don't have the temperature coefficient of R1

I know this may look silly because it maybe very easy to all of you
but please help me on this
 
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  • #2
We're not talking about two different components R2 and R1.

We're talking about the same component, which has two different resistances at two different temperatures.

R1 is the resistance at temperature T1

R2 is the resistance at temperature T2.

You can confirm this by noticing that if T2 = T1, then delta T = 0, and hence R2 = R1.

In this case, delta T = T2 - T1 = 80 C - 10 C = 70 C, and you already know R1, which is the resistance at T1 = 10 C. So all you have to do is use the equation to solve for R2.
 
  • #3
cepheid said:
We're not talking about two different components R2 and R1.

We're talking about the same component, which has two different resistances at two different temperatures.

R1 is the resistance at temperature T1

R2 is the resistance at temperature T2.

You can confirm this by noticing that if T2 = T1, then delta T = 0, and hence R2 = R1.

In this case, delta T = T2 - T1 = 80 C - 10 C = 70 C, and you already know R1, which is the resistance at T1 = 10 C. So all you have to do is use the equation to solve for R2.

but how about the [itex]\alpha[/itex]1
I can use the coefficient at 0 C to solve different temperature?
 
  • #4
Rito3d03 said:
but how about the [itex]\alpha[/itex]1
I can use the coefficient at 0 C to solve different temperature?

I think you can assume alpha is constant. It's not strictly true, but the linearity holds within a certain temperature range around the temperature at which the coefficient was measured. 80 degrees may seem like a fairly large range, but unless you've been given additional information about how the alpha coefficient itself varies, I don't see any other choice other than using the given value and assuming it to be constant with temperature.
 
  • #5
I finally find out the way to solve this question
first find out R0 which is the resistance at 0°C
10 = R0 (1+0.00393*(10-0))
then I can use the equation to solve the rest of the problem
and figure out R80
R80= R0 (1+0.00393*(80-0))

I guess i was stuck on some logic problem
glad i can finally finish this and move on
thanks for the help
 

Related to Resistance problem (Simple electrical problem)

What is resistance?

Resistance is a measure of how much a material or component resists the flow of electricity. It is measured in ohms (Ω).

What causes resistance?

Resistance is caused by the collision of electrons with the atoms of a material. Materials with tightly packed atoms, such as metals, have low resistance, while materials with loosely packed atoms, such as rubber, have high resistance.

How is resistance calculated?

The resistance of a material or component can be calculated using Ohm's Law (R=V/I), where R is resistance, V is voltage, and I is current. Resistance can also be calculated using the equation R = ρL/A, where ρ is the resistivity of the material, L is the length of the material, and A is the cross-sectional area.

What is the relationship between resistance and current?

According to Ohm's Law, resistance and current have an inverse relationship. This means that as resistance increases, current decreases, and vice versa.

How do you measure resistance?

Resistance can be measured using a multimeter, which measures the voltage and current of a circuit and calculates the resistance. Alternatively, resistance can be measured using an ohmmeter, which applies a known voltage to the circuit and measures the resulting current.

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