Relationship between material resistance and temperature

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Discussion Overview

The discussion revolves around the relationship between material resistance and temperature in the context of heater plates. Participants explore how resistance affects power dissipation and temperature rise when a current is passed through materials, considering different scenarios of constant voltage and current.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that for a given power, higher resistance might lead to higher temperature, while others challenge this by stating that higher resistance results in lower power for a constant voltage.
  • One participant clarifies that power can be expressed as P = I^2R or P = V^2/R, leading to different interpretations based on whether current or voltage is held constant.
  • It is noted that in most cases, with constant voltage, power is inversely proportional to resistance, suggesting that lower resistance would lead to higher power and thus higher temperature.
  • Another participant expresses confusion about the relationship between heat and power, specifically questioning which heater plate would heat more under constant voltage conditions.
  • Some participants agree that with constant voltage, the heater plate with lower resistance would heat to a higher temperature over time, assuming other factors remain constant.
  • One participant introduces the concept of energy conservation, linking electrical energy transfer to heat energy through electron collisions with the ionic lattice, which increases thermal vibrations and temperature.

Areas of Agreement / Disagreement

Participants generally express disagreement regarding the relationship between resistance and temperature, with multiple competing views on how power dissipation relates to resistance under different conditions. The discussion remains unresolved as participants explore various scenarios without reaching a consensus.

Contextual Notes

Participants highlight the importance of keeping either voltage or current constant when discussing resistance and power, indicating that the relationship is not straightforward and depends on the specific conditions of the experiment.

rede96
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For the material used in a heater plate to generate heat for example, for a given amount of power (say 4.5 kw) does the higher resistance of the material mean it will produce a higher temperature? Or is it the other way around?
 
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Not completely clear to me what you mean. For a given voltage, the power dissipated in a heating wire is ##P = I \times V = V^2/R##, so a higher resistance leads to a lower power.
 
BvU said:
Not completely clear to me what you mean. For a given voltage, the power dissipated in a heating wire is ##P = I \times V = V^2/R##, so a higher resistance leads to a lower power.

Thanks for the reply. Basically I wanted to know for a given resistance in a material if I pass a current through it will materials of a higher resistance get hotter than those with lower resistance.

Taking ##P = I \times V## and Ohm's law ##V = IR## and eliminating the ##V## then ##I^2R## is the way the power is distributed. So heat (power) is proportional to resistance, i.e. the more resistance the more heat? But I haven't done any of this for such a long time I'm just not sure if that's right.
 
You can write...

P=I^2R which suggests P is proportional to R
or
P=V^2/R which suggests P is proportional to 1/R

The apparent contradiction occurs because the variables are not independent.

The answer to your question is... It depends what you keep constant (I or V) when you change R. You cannot keep both constant.
 
In most cases the voltage is constant (for example the mains voltage is fixed at 110V or 220V). In that case power is proportional to 1/R.

It a few cases the current is constant (for example some types of battery charger). In that case power is proportional to R.
 
CWatters said:
In most cases the voltage is constant (for example the mains voltage is fixed at 110V or 220V). In that case power is proportional to 1/R.

It a few cases the current is constant (for example some types of battery charger). In that case power is proportional to R.

I might be getting mixed up with heat and power. Basically what I was interested in knowing, assuming a constant voltage, is if I have two heater plates one with a higher rated resistance than the other. Which would heat up more? I thought it’d be the one with the higher resistance?
 
See post #2. A lower resistance means a higher current. With the same voltage, the product I x V is then higher.

Power I x V is heat dissipated per unit time
 
BvU said:
See post #2. A lower resistance means a higher current. With the same voltage, the product I x V is then higher.

Power I x V is heat dissipated per unit time

Right, got it thanks. So for two heater plates given the same voltage the one with the lower resistance will heat to a higher temperature in the same time frame.
 
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BvU said:
Not completely clear to me what you mean. For a given voltage, the power dissipated in a heating wire is ##P = I \times V = V^2/R##, so a higher resistance leads to a lower power.
Then with the conservation of energy principle this would be a case of electrical energy transferred to heat energy. The conduction electrons collide with the ionic lattice (resistance) this increases amplitude of thermal lattice vibrations corresponding to temperature increase.
 
Last edited:
  • #10
rede96 said:
Right, got it thanks. So for two heater plates given the same voltage the one with the lower resistance will heat to a higher temperature in the same time frame.
That's correct (if we assume everything else is the same, such as the thermal properties of the heat plates).
 

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