# very simple question

Discussion in 'General Electronics Chat' started by PSnetwork, Dec 4, 2013.

1. ### PSnetwork Thread Starter Member

Apr 1, 2013
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can someone help me with that question:

Show that it is not possible to exceed the power rating of 1/4 watt resistor
of resistance greater than 1k, no matter how you connect it, in a circuit operating from a 15 volt battery.

thanks.

Last edited: Dec 4, 2013
2. ### shteii01 AAC Fanatic!

Feb 19, 2010
3,392
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LOL
You have to be more subtle than that!

3. ### shteii01 AAC Fanatic!

Feb 19, 2010
3,392
497
Do the math.
The worst I got so far is 0.225 Watt. Which is less than 0.25 Watt.

4. ### w2aew Member

Jan 3, 2012
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The question is flawed.

Certainly, if the worst case power dissipation of a 1K resistor in a 15V circuit would be if the resistor is directly across the supply - and the result is under 250mW (V^2/R).

However, it is certainly possible to build a circuit that is powered by 15V that generates a higher voltage (a DC to DC converter for example), where you could easily smoke a 1/4W 1kOhm resistor...

PSnetwork likes this.
5. ### BReeves Member

Nov 24, 2012
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The kicker is "Greater than 1K". with the help of an old guy named Ohm it's pretty simple.

6. ### bountyhunter Well-Known Member

Sep 7, 2009
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Correct. At room temp ambient, the resistor should survive.

7. ### WBahn Moderator

Mar 31, 2012
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Yes. True. But some common sense needs to be applied. At what level of electronic education would a question like this be asked? Would someone at that level likely even know about power sources other than simple DC sources?

Nov 7, 2013
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9. ### inwo Well-Known Member

Nov 7, 2013
2,433
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Power is E squared divided by the resistance. A graph would show as you get over 1K, power dissipated is dropping below 1/4 watt.

10. ### THE_RB AAC Fanatic!

Feb 11, 2008
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The "1/4 watt" power rating is for typical use in free air, and with some modern smaller package resistors might even require some cooling into the PCB copper to get 1/4 watt.

If the resistor was encapsulated, or right next to a heatsink etc it may need to be de-rated significantly.

11. ### WBahn Moderator

Mar 31, 2012
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Beyond the scope of the question.

inwo likes this.
12. ### PSnetwork Thread Starter Member

Apr 1, 2013
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This question is from "The art of electronics" second edition book. thats from the very beginning of the book.

13. ### WBahn Moderator

Mar 31, 2012
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Ah. That would have been handy to know just to set the context. I haven't looked at AoE for some years, but I'm guessing that, at the point where that is asked, about all that has been introduced are batteries and resistors and not much else.

PSnetwork likes this.
14. ### BReeves Member

Nov 24, 2012
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From the OP "in a circuit operating from a 15 volt battery".

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15. ### wayneh Expert

Sep 9, 2010
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I hate these kind of questions, that assume but do not state a context. As a chemical engineer, I might approach this problem as "Can you construct a circuit to use energy from the battery to roast this resistor?" Just because YOU haven't taught me how to do it doesn't mean I don't know, in principle, how to do it.

Thankfully, assuming simplicity ("Aha, this is an Ohm's law question!") is usually the right strategy on these questions. Don't overthink them unless there are clues that you must.

atferrari likes this.
16. ### THE_RB AAC Fanatic!

Feb 11, 2008
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But still well worth mentioning!

People may read this and get the impression a 1/4 watt resistor can always dissipate 1/4 watt safely. That is not a fact.

Especially when the OP used terms like "not possible to exceed the power rating" and "no matter how you connect it".

17. ### bountyhunter Well-Known Member

Sep 7, 2009
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+1 I could not count the number of times people who design electronics forget one simple thing: the air outside the unit may be 20C, but inside it is always hotter. You have to derate components used in virtually any electronic device made on earth.

An even more sneaky problem: with the presnt day surface mount universe, power devices use the PCB and copper traces to dissipate heat..... so the active devices pump heat into the board and the other parts go for the ride. Even if the air is cool, a part next to a power device may be getting cooked by the heat generated next door.

It's a complicated world when it comes to power derating....

18. ### WBahn Moderator

Mar 31, 2012
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So, just to be sure I understand. The concern is that someone might get the impression that a 1/4 W resistor can always safely dissipate 1/4 W. So, by pointing out that a 15V-battery powered circuit can be designed so as to apply more than 15V to a 1kΩ resistor and thereby raise its power dissipation above its 1/4 W rating will ensure that no one will get the impression that a 1/4 W resistor can always dissipate 1/4 W safely.

Interesting. I don't quite see the reasoning, but interesting chain of logic.

I suppose we should also consider that a 10MΩ 1/4 W resistor would have nearly 1600V across it when it is dissipating 1/4 W. So since we need to be concerned that someone might get the impression that a 1/4 W resistor can always dissipate 1/4 W safely, we should point this out since working around a resistor that has 1600V across it may well not be very safe.

19. ### WBahn Moderator

Mar 31, 2012
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Yes. And every person that is in the first few pages of an electronics text and just learning what a resistor is and about Ohm's Law and about power in a resistor should simultaneously be expected to deal with power derating.

20. ### GopherT AAC Fanatic!

Nov 23, 2012
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So you are implying that ohms law cannot be supplied to a circuit because someone may have slipped a DC/DC converter circuit between the stated voltage source and the ressitor?

Don't you think that a reasonable enough to ask this question would be knowledge enough to notice a DC/DC converter between the voltage source and the resistor?