Joule heating effect - qualitative explanation

[dwd40physics]

Homework Statement

Explain why heating elements use resistance of low resistance rather than high resistance.

Relevant Equations

P = I^2 x R

Hi,

I understand mathematically why using low resistance results in a greater heating effect. Could someone give an intuitive and microscopic picture of why the current contributes more to a greater power dissipation by the resistor rather than the resistance contribution to the power dissipation.

I understand by proportionality (V=IR) that if you half the resistance across the load (resistor) the current doubles. Since P = I^2 x R the power dissipated is a factor of 2 greater (factor 4 for the current and factor 1/2 for the resistance).

The model I use is that electrons collide with lattice atoms and convert their KE to the lattice atoms and thus cause the heating element (resistor) to heat up. Can someone explain how this differs from using a high resistance where I assume that the heating effect due to lattice vibrations would be greater? What makes using a low resistance better than a high resistance.

Many thanks.

 

[DEvens]

Does this thread https://www.physicsforums.com/threads/resistance-of-a-heating-element.5608/ cover it?

 

[dwd40physics]

Hi, I've seen this thread before. Re-reading it has definitely helped however it still does not completely resolve my issue. Too much reliance on algebraic explanations.

Thanks nonetheless :)

 

[DaveE]

Homework Statement: Explain why heating elements use resistance of low resistance rather than high resistance.
Homework Equations: P = I^2 x R

Is that the whole problem statement? If so, I'll avoid (with great effort) giving y'all a rant about bad homework questions.
Given the equations V = I⋅R and P = V⋅I, you can easily calculate what you need to know for a well specified problem of this type.
In the real world, we would start with what is the nature of the electric energy source and how much heat is required. Lower isn't always better, higher isn't always better. Engineers will calculate the optimum value given the problem constraints.

 

[dwd40physics]

Is that the whole problem statement? If so, I'll avoid (with great effort) giving y'all a rant about bad homework questions.
Given the equations V = I⋅R and P = V⋅I, you can easily calculate what you need to know for a well specified problem of this type.
In the real world, we would start with what is the nature of the electric energy source and how much heat is required. Lower isn't always better, higher isn't always better. Engineers will calculate the optimum value given the problem constraints.

Hi, thanks yes just wanted an intuitive explanation of specifically why the resistance is low.

 

[DaveE]

Hi, thanks yes just wanted an intuitive explanation of specifically why the resistance is low.

Sorry, maybe someone else can do that. I think these equations are so simple that intuition isn't required. Or, perhaps I should say that the equations are the intuition.
Anyway, what is low? 100ohms? 10ohms? 1ohm? 0.01ohms? Low compared to what, specifically?
I think you have what you need for the answer, but you are lacking a well defined question.

 

[DEvens]

Hi, thanks yes just wanted an intuitive explanation of specifically why the resistance is low.

How much more intuitive than P=V^2/R would you require?

 

[dwd40physics]

Hi yes I would go for the equation when explaining it however, I'm explaining this to 12-13 year olds so I was trying to get a good explanation for why the resistance is low.

 

[DaveE]

Hi yes I would go for the equation when explaining it however, I'm explaining this to 12-13 year olds so I was trying to get a good explanation for why the resistance is low.

OK but, low compared to what? I think you will just be confusing them without more of a framework to fit this into. After all of these posts, I still don't know if you think 10ohms is a high or a low value. In fact you haven't even specified what sort of power source you have. For a current source (like some PV configurations) the power will decrease as you reduce the resistance.
If they aren't ready for the equations defining resistance and power, then they aren't ready for your high/low resistance question. If they are ready for those definitions than why not show them some design examples with numbers and then talk about the dependence of power on resistance. Something like given a 120V source, graph the current and power in a 100, 50, 20, 10, 5, 2, or 1ohm resistor.