inversely or directly

Hi to all,
We are having a debate at my school about the correct answer on a test we had. The question was “How does the heat dissipated in a resistor vary with the resistance when the voltage is held constant?” We have 2 instructors that are in disagreement with the answers. The 2 answers we are in deadlock with are directly or inversely. Any help would be greatly appreciated. One instructor explains it as when you have a resistor of a smaller size such as 100 ohms will give off more heat than a 10 k ohm resistor because more current will be flowing through the 100 ohm which to him is inversely because of the more amps with less resistance. The other instructor says that it is directly because the resistor gives off more heat as the amps increase. Which one is correct? Please help me.

Have your instructors tried using any sorts of formulas?

As I recall, P = (V^2 / R). There is an obvious inverse relationship between reistance and power.
The question makes no mention of current.

A debate between instructors regarding such a simple concept would make me seriously question the quality of education that they could provide.

For the question you quoted: “How does the heat dissipated in a resistor vary with the resistance when the voltage is held constant?”

The answer would be inversely since it refers to the relationship between heat and resistance, not current.

Less resistance equals more heat...more resistance, less heat.

My take on it is using ohms law with 1 constant and 2 varying,
Voltage, Amps, Resistance.

Then you are looking at the relationship of the 2 varying
voltage and current varying will be directly
resistance and amps or resistance and volts varying will be inverse

Now is the mud any clearer.
It really depends on where you are looking at the issue from.

P = (I^2) * R , V=I * R

w/ voltage held constant, I will drop as R rises
P will drop as R rises. P dissipated across a resistor turns to heat.

Maintenance Man said:

Thank you all for your help. I am partial to inversely because it is asking about heat and resistance. The instructor who said inversely explained it more in terms that I understood. The education we are receiving is top notch. This is the first time I have seen them disagree.

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I guess we all have our moments of stupidity. Glad to hear that we could help to make things more clear (or at least confirm your suspicions)

In this situation, there can be only one answer: Inversely
Less Resistance --- More Heat

Im more amazed that those instructors could't find right answer by themselves. That does not tell well about their capabilites to develop as instructors..

Maintenance Man said:

The other instructor says that it is directly because the resistor gives off more heat as the amps increase.

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Tell this guy to re-read what he is saying. He has the reasoning right but the conclusion wrong. I am in agreement that the more puzzling part is how any sort of engineering professor could find this confusing. And why they would ever admit to "debating" about this in front of their students!

I really don't want to hijack this thread – but here's a story sort of along the same lines ...

back when I used to work for a systems integrator one of my assignments was to reassemble an ancient relic of a machine from a foreign country that had absolutely ZERO documentation available ... one of the components was an electrical clutch – and we had no way of knowing how much voltage to apply to it ...

I told my boss (an engineer) that I planned to temporarily hook the coil up to a variable transformer – and then to experiment by slowly increasing the voltage until the magnet pulled in the armature ...

"Of course I'll put an ammeter in the circuit to make sure that the amps don't go too high when I crank the voltage up." ...

my boss quickly corrected me ...

"Ron, you've got it backwards. When the voltage goes UP, the amps will go DOWN." ...

this wasn't the sort of boss you could laugh at – and I could tell that he was dead serious ... so I asked him if he was sure about this ...

"Absolutely. That's why the power company runs their cross-country transmission lines at about 30,000 volts. The higher voltage makes the amps real low – so that they can get away with using much smaller wires. So as the volts go UP, the amps go DOWN." ...

yet another case of "knowing the rules" – but not knowing how to apply them ...

Maintenance Man said:

“How does the heat dissipated in a resistor vary with the resistance when the voltage is held constant?”

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I'm just a simple Mechanical Engineer but I did have some heat transfer classes in school so I'm going to take a crack at this.

My first thought was: The question is bogus! You do not have enough information to answer the question as posed. Heat dissipation is related to the materials the resistor is made of, the temperature difference between the ambient air and the internal temperature of the resistor and the speed of the air moving past the resistor.

But, then I found this site:
http://www.pa.msu.edu/courses/1997spring/phy232/lectures/resistors/power.html
(Like I said, I'm a mechanical engineer, not an electrical engineer )

So, straightening my thinking cap, assuming the resistor is not failing, all heat generated must be dissipated embar so back to the equation in the above link.
P=IV

V is not changing and by Ohm's Law, I = V/R so:

P=(V^2)/R

The left side is energy/power/heat and on the right side, Resistance is in the denominator so I'd say the proper answer is:

Inverse

maybe this is what they're up to? ...

from jonnies ...

And why they would ever admit to "debating" about this in front of their students!

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well, maybe it's a case of "Socratic Irony" ... named after that old Greek guy Socrates - from about 2500 years ago ...

http://www.sarcasmsociety.com/irony/socratic

(or in other words, sort of like the PLC Boot Camp approach) ...

Instructor1 said:

One instructor explains it as when you have a resistor of a smaller size such as 100 ohms will give off more heat than a 10 k ohm resistor because more current will be flowing through the 100 ohm which to him is inversely because of the more amps with less resistance.

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TRUE

Instructor2 said:

the resistor gives off more heat as the amps increase.

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This is also true. However, interpretation is wrong. Did you ever wonder how kitchen electric cooker works?

Why you can have 200°C in the oven with switch in position A and 300 °C in the oven when the switch in position B?

Elements that are supposed to produce heat (heaters) have small resistance.
Key is the constant voltage. You have constant voltage in your home.