Resistance depending on temperature

In summary, the resistance of a segment of gold wire at 30.3C is 124.9 omega, but when placed in a liquid bath, it decreases to 97.5 omega. The temperature of the bath can be calculated using the equation R=Ro[1+alpha(t-to)], where Ro is the initial resistance at 20C and alpha is the temperature coefficient for gold. The correct answer is less than -34.22C, with two significant figures. It is possible that the incorrect answer was due to not considering significant figures.
  • #1
lilaznjewel
13
0

Homework Statement



At 30.3C, the resistance of a segment of gold
wire is 124.9 omega When the wire is placed in a
liquid bath, the resistance decreases to 97.5 omega
What is the temperature of the bath?
The temperature coefficient for gold is
0.0034 (C)−1 at 20C.
Answer in units of C.


Homework Equations



used R=Ro[1+alpha(t-to)

The Attempt at a Solution



I got -34.2, but the homework says its incorrect
 
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  • #2
Hmm. The numbers look okay to me. Did you include the units when you answered?
 
  • #3
gneill said:
Hmm. The numbers look okay to me. Did you include the units when you answered?

yes do you think it could be wrong because of sigfigs so it be -34.22
 
  • #4
How many significant figures do each of the provided numbers have?
 
  • #5
To has 3
Ro has 4
R has 3
alpha has 4
 
  • #6
Check http://www.usca.edu/chemistry/genchem/sigfig.htm" .
 
Last edited by a moderator:
  • #7
ok i put in -34.22 but, it is still wrong
 
  • #8
-34.22 has four significant figures. The temperature coefficient has fewer.
 
  • #9
I'm getting something else ... its less than your answer

why not use the temp you got and find the resistance and match it with 124.9 ohm
 
  • #10
I don't really understand what you are trying to say
 
  • #11
The provided temperature coefficient for gold has two significant figures. Did you try your result with two significant figures?
 

FAQ: Resistance depending on temperature

1. How does resistance change with temperature?

As temperature increases, the resistance of most materials also increases. This is due to the increase in the random thermal motion of the atoms, which causes more collisions and obstacles for the flow of electrons.

2. What is the relationship between resistance and temperature?

The relationship between resistance and temperature is often described by the equation R = R₀ (1 + αΔT), where R is the resistance at a given temperature, R₀ is the resistance at a reference temperature, α is the temperature coefficient of resistance, and ΔT is the change in temperature. This equation shows that resistance is directly proportional to temperature.

3. Why does resistance decrease at low temperatures?

Some materials, such as superconductors, exhibit a decrease in resistance at low temperatures. This is because at very low temperatures, the thermal motion of the atoms decreases, allowing for the flow of electrons with minimal resistance.

4. How does the temperature coefficient of resistance vary between materials?

The temperature coefficient of resistance, α, varies between materials and is often dependent on the type and properties of the material. For example, metals typically have a positive temperature coefficient, while semiconductors may have a negative temperature coefficient.

5. How does temperature affect the resistance of a circuit?

In a circuit, the total resistance is affected by the individual resistances of each component, as well as the temperature coefficient of each component. As the temperature changes, the resistance of each component will change, leading to an overall change in the resistance of the circuit.

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