Relationship between material resistance and temperature

In summary, for a given amount of power, the higher resistance of a heater plate will lead to a lower temperature, while a lower resistance will lead to a higher temperature, when keeping the voltage constant. This is due to the relationship between power, voltage, and resistance, where a higher resistance leads to a lower power. This is because the power dissipated in a heating wire is proportional to the resistance, and the conservation of energy principle explains that this is due to the electrical energy being transferred to heat energy through collisions between the conduction electrons and the ionic lattice.
  • #1
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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
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?
 
  • #7
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
 
  • #8
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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  • #9
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.
 
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  • #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).
 

1. What is the relationship between material resistance and temperature?

The relationship between material resistance and temperature is that as temperature increases, the resistance of a material also increases. This is known as positive temperature coefficient (PTC). Conversely, as temperature decreases, the resistance decreases as well, which is known as negative temperature coefficient (NTC).

2. Why does material resistance change with temperature?

Material resistance changes with temperature because as the temperature increases, the atoms in the material vibrate more and collide with electrons, making it more difficult for them to flow. This results in an increase in resistance. Conversely, as temperature decreases, the atoms vibrate less, allowing for easier electron flow and a decrease in resistance.

3. How does the type of material affect its resistance at different temperatures?

The type of material plays a significant role in its resistance at different temperatures. Conductors, like metals, have low resistance at room temperature and become more resistant at higher temperatures. Insulators, like rubber, have high resistance at room temperature and become less resistant at higher temperatures. Semiconductors, like silicon, have a more complex relationship with temperature, but generally have an increase in resistance as temperature increases.

4. What is the practical application of understanding the relationship between material resistance and temperature?

Understanding the relationship between material resistance and temperature is crucial for designing and operating electronic devices. It allows engineers to select the appropriate materials for different temperature ranges and ensure the proper functioning of the device. It also helps in predicting and monitoring the performance of electronic components in various environments.

5. How can we measure the change in resistance due to temperature?

The change in resistance due to temperature can be measured using a thermometer and a multimeter. The thermometer is used to measure the temperature of the material, while the multimeter can measure the resistance of the material. By taking multiple measurements at different temperatures, the relationship between resistance and temperature can be determined.

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