Calculating Temperature Rise of a Resistor

Long story short, I have a load bank using resistors. To get the right vale resistors, there are various combinations of 1-4 resistors in combinations of up to two parallel pairs in series.

In particular, one load option is deisgn for 4 volts at 160mA (25 ohms) It actually consists of a 10 ohm and a 15 ohm resistors in series.

Voltage measurement across the resistors reads 3.74V, with 1.48V across the 10ohm and 2.22V across the 15ohm.

The design power calculations are
10ohm is 0.256W
15ohm is 0.384W

I used 1/2 Watt resistors for both. I can only touch them long enough to tell I can't touch them. I know touch is a poor determination of actual temperature.

How do I determine an estimate for the temperature rise of each resistor given the numbers above? (unfortunately I don't have a IR temp gun) Before this gets off into the discussion on how they are mounted, etc. The are spaced away from the board. I was not silly enough to have them lay on the board as they are normally installed. There is, quite literally, 1/2" of lead on both ends between the resistor and the board.

At what point should I be concerned? Normally I don't like my electronics to get hotter than I can touch, but this is a load bank. It is supposed to get warm. Warm, not expecting hot. In terms of wattage, the 10ohm is at 50% and the 15ohm at 76%. Off my cuff, I would think that's plenty, but these are hot.

On the cuff, that's not plenty.

A good rule of thumb for long term reliability of electronic components is to run them at no more than 50% of their rating. No more than .25 W dissipated in a .5 W resistor, no more than 30 V across a 60 V power MOSFET, etc. Some parts, like AC powerline X and Y capacitors, are designed to be run continuously very near their voltage rating. But most parts have a significantly longer lifetime with derating. The US military and the telecom industry have strong recommendations about this, and many large electronics companies have fairly strict in-house standards.

ak

Look up the data sheet on your resistors. There should be curves like this.

ronsimpson said:

Look up the data sheet on your resistors. There should be curves like this.

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I hit up google before I posted. Unfortunately I purchase from surplus suppliers so I don't know the exact manufacturer. I did a google search and found websites for Riedon, Vishay.Dale, Ohmite, and Caddock. None of them provided any information related to the second chart or thermal characterization (degC / W). From whom did you find the second chart?

first data sheet I looked for, see attached.
I think they should have (degC / W).

ronsimpson said:

I think they should have (degC / W).

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One would think so, but I don't see it. That's the only datasheet that has that graph for metal or carbon film resistors. The datasheets for the "true" power resistors (sandstone, etc) have a whole bunch more other information.

Based on the reply from AnalogKid, I'm thinking the resistors that are 50%, especially those over 60%, need to be sized up.

ADWSystems said:

I'm thinking the resistors that are 50%, especially those over 60%, need to be sized up.

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Depends upon how long this load bank is intended to operate.
If not for a long time (months), than I would think you could readily operate to 75% of the resistor power rating (as long as it's in free air and not closely adjacent to other resistors).

It Isn't just the Rating for the Resistor, It is also Where it will be used.
In an Enclosed Space with Poor Ventilation, Heat can Build Up quickly.

crutschow said:

Depends upon how long this load bank is intended to operate.
If not for a long time (months), than I would think you could readily operate to 75% of the resistor power rating (as long as it's in free air and not closely adjacent to other resistors).

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chemelec said:

It Isn't just the Rating for the Resistor, It is also Where it will be used.
In an Enclosed Space with Poor Ventilation, Heat can Build Up quickly.

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I have tried to take all of that into account. The resistors are 1/4" apart and 1/4" from the board. The enclosure is louvered and , I would call, spacious. I plan to add a small fan. One test is estimated to take 10-12 hours. The down time between tests depends on exactly when the previous test finishes. It could be minutes or hours.

ADWSystems said:

From whom did you find the second chart?

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Digikey.com

In the 70s I installed many very high end real to real tape decks in a wall of electronics. (early automatic radio station, no person on duty) On the first hot summer day the tap decks stopped working one at a time. The 10 watt power resistors were falling out of the PCBs. The "rated max temp" for the resistors was above the milting point of solder. Just because the resistor can withstand the temperature that does not mean the PCB, solder, or near by parts can withstand the temp.

Temperature Kills.

ronsimpson said:

Digikey.com

In the 70s I installed many very high end real to real tape decks in a wall of electronics. (early automatic radio station, no person on duty) On the first hot summer day the tap decks stopped working one at a time. The 10 watt power resistors were falling out of the PCBs. The "rated max temp" for the resistors was above the milting point of solder. Just because the resistor can withstand the temperature that does not mean the PCB, solder, or near by parts can withstand the temp.

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True True. Been there seen that (at least with the temperature exceeding the melting point of the solder).

My intention was to indicate that there was airflow beneath the resistors for improved heat dissipation.

From Yageo resistors:
At 155C the resistor has a 0 watts rating. So that is to say that this resistor should not get above 155C.
I think at 70C air temp and 100% power the body of the resistor is at 155C.
So (155-70=85) My guess is that 100% power causes a temp rise if 85C.

ronsimpson said:

From Yageo resistors:
At 155C the resistor has a 0 watts rating. So that is to say that this resistor should not get above 155C.
I think at 70C air temp and 100% power the body of the resistor is at 155C.
So (155-70=85) My guess is that 100% power causes a temp rise if 85C.

View attachment 115810

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I really hope air temp isn't 70 degC. LOL.

I'm not so sure we can make the leap that 100% power causes the resistor to rise to 155 degC. Seems like a second leap of logic mixed in there.

I agree that at 155 degC the resistor cannot dissipate any heat. That's in the chart, indisputable. But it cannot be said that 100% power usage will drive the resistor to 155 degC. At 70 degC, you have 100% of the power rating. At 120degC the resistor is now only 40% of the specified wattage rating (turning a 1W resistor into a 0.40W resistor).

I don't see anything there that indicates what the temperature rise of the resistor will be based on the load (amount of wattage used). The key there is to get the package thermal characteristics (degC/watt).

ADWSystems said:

I agree that at 155 degC the resistor cannot dissipate any heat. That's in the chart, indisputable. But it cannot be said that 100% power usage will drive the resistor to 155 degC. At 70 degC, you have 100% of the power rating. At 120degC the resistor is now only 40% of the specified wattage rating (turning a 1W resistor into a 0.40W resistor).

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That's correct.
But assuming a full power body temperature of 155°C at a 70°C ambient is what the graph is showing.
A linear derating from 70°C to 155°C, with the body temperature staying at 155°C will give a power rating of 40% of the value at 70°C for an ambient of 120°C.
Why do you think otherwise?

crutschow said:

That's correct.
But assuming a full power body temperature of 155°C at a 70°C ambient is what the graph is showing.
A linear derating from 70°C to 155°C, with the body temperature staying at 155°C will give a power rating of 40% of the value at 70°C for an ambient of 120°C.
Why do you think otherwise?

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You are listing three variables on a 2-D graph. The graph is ambient temperature vs. rated power. There is no place for body temperature in the graph.

ADWSystems said:

There is no place for body temperature in the graph.

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At 150C ambient and no power we know the body temp is 155.
At 70C ambient and no power we know the body temp is 70. (at 0W we know the body temp = ambient)
I made an assumption: At 70 ambient and full power, body = 155. I assume this based on the idea that '155 body is max' at any power level. Reading between the lines, I think 85C rise in temp is for 100% power. (42.5C for 1/2 power. 21C for 1/4 power, etc)

We can derive body temp by (ambient + (85C X (percent power)))

ronsimpson said:

At 155C ambient and no power we know the body temp is 155.
At 70C ambient and no power we know the body temp is 70. (at 0W we know the body temp = ambient)

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I can agree with both of those statements. No power dissipated means amibient temp equals body temp.

At 155degC the resistor cannot dissipate any heat (has 0W rating, ie. useless)

ronsimpson said:

I made an assumption: At 70 ambient and full power, body = 155. I assume this based on the idea that '155 body is max' at any power level. Reading between the lines, I think 85C rise in temp is for 100% power. (42.5C for 1/2 power. 21C for 1/4 power, etc)

We can derive body temp by (ambient + (85C X (percent power)))

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This section I don't agree with. The graph states ambient temperature versus wattage. If the ambient is 70degC then the resistor is rated for 1W. It doesn't say body temperature versus wattage.

If I extrapolate your equation, then the resistor is NEVER usable at 1W. At 0degC and 100% power the body temperature would be 85degC and knocked down to 80% wattage. This would not be a very useful device, as there would be no way to use it at 100% power. In summary the body temperature cannot be inferred from the graph of ambient versus wattage rating.

My equation may be wrong, but the resistor can do full power at 70 air temp. There is a triangle bordered by 70@100, 155@0, and 155@100. This is typical of heating elements.

I see your logic. The equation you propose is correct (or matches your logic). 100%

But I think it is a leap to say that at 100% of the rated power the body temperature will rise 85degC. But with that said, that is the question. At a given ambient temperature for a rated power dissipation, what is the expected rise in body temperature. TO-220 transistors give this information under thermal characteristics in the line item degC/W. I think the same thermal characteristic is needed here. But I have been unable to find it.

ADWSystems said:

degC/W. I think the same thermal characteristic is needed here. But I have been unable to find it.

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ADWSystems said:

will rise 85degC.

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85C/Full Power