Question about resistor power rating?

[AlNewman]

Hi,
So I ordered a few resistors to create a dummy load box, and I want to understand how the power ratings change with the resistors placed in series and parallel.  I ordered 2x4 ohm@50 watt, and 2x8 ohm@ 50 watt.  I'm hoping to build something that can be used for 2, 4, 8, and 16 ohm.

So, unless I misunderstand what I'm reading, the power ratings are always accumulative?
Eg:
2+4 ohm in parallel=2 ohm@100w
2x8 ohm in series=16 ohm@100w
1x8 ohm in parallel with 2x4 ohm in series=4 ohm@ 150 watts?

Something seems wrong to me.  I would think that in series, the power rating would diminish, and in parallel it would increase, but it's hard to find (or maybe understand) the theories on how resistance power ratings change, although there is lots of information on how the values affect one another between series and parallel.

Help me out with a grade 10 physics question?

[nandrewjackson]

Your first 2 examples are correct.
The 3rd is not.


In the 3rd example the single 8 ohm R will receive half the current, but it's maximum power is still 50W.
The 2 series 4 ohms will receive half the current, but *their* power capacity is now 100W.


That example should only be fed 100W input maximum due to the single 8 ohm R still receiving half the current.


If example 3 was fed 150W, the single 8 ohm resistor would get half the current, and run at 75 watts.


Feeding example 3 with 150 W would spell trouble for the single 8 ohm resistor.

[AlNewman]

Awesome, thank you very much.
So no matter what, the total wattage is determined by the capacity of one leg of a parallel circuit.  So I would have been better off, since I bought 4 resistors, to have just bought 4 4 ohm then.  Interesting.

[sluckey]

So no matter what, the total wattage is determined by the capacity of one leg of a parallel circuit.

No. You must analyze each parallel leg separately.

[HotBluePlates]

... So no matter what, the total wattage is determined by the capacity of one leg of a parallel circuit. ...

No. You must analyze each parallel leg separately.

This is a great time to work through Chapter 3 of NEETS Module 1.

It includes examples of different "Ohm's Law puzzles" that will help you see how Volts and Current get divided among different parts.  And also why it rarely works to seek a "simple rule" for judging power-handling capacity.

[AlNewman]

No. You must analyze each parallel leg separately.

Ok.
But the total dissipation is dependent on the weakest link?

So best case scenario, as I have 2x4 ohm@ 50 watt and 2x8 ohm@ 50 watt...

2 ohm load=2x4 ohm in parallel@100 watt max dissipation.
4 ohm load=2x8 ohm in parallel@100 watt
8 ohm load=2x4 ohm in series @100 watt
16 ohm load=2x8 ohm in series@100 watt

Is this correct?

[AlNewman]

This is a great time to work through Chapter 3 of NEETS Module 1.

It includes examples of different "Ohm's Law puzzles" that will help you see how Volts and Current get divided among different parts.  And also why it rarely works to seek a "simple rule" for judging power-handling capacity.

That's a great link.  I kind of enjoy taking little bites, and then falling into the rabbit hole as time and energy permits, but you have given me a full on unclassified superhighway of information.  I'll probably print it out, and refer to it again and again.  Thank you.

[PRR]

Chipmunks must have been eating {quote} tags. I inserted some, I hope in right places.

[thetragichero]

This is a great time to work through Chapter 3 of NEETS Module 1.

man that NEETS course is... neat
goes from "what is an atom" all the way to radar and microwave if you choose to read the far (i did not. only really concerned with making guitar go BRRRRRRRR)

[shooter]

ARGG metered internet

[shooter]

that NEETS course is... neat

that was school 1 of 4 when I went through the Navy's advanced electronics program.  You got 12 modules, 12 weeks, you taught yourself.
the fail rate was 50%, most of the fail was being 18 and no parental supervision
I made it through since I had no parental supervision early on in life 

[AlNewman]

that NEETS course is... neat

that was school 1 of 4 when I went through the Navy's advanced electronics program.  You got 12 modules, 12 weeks, you taught yourself.
the fail rate was 50%, most of the fail was being 18 and no parental supervision
I made it through since I had no parental supervision early on in life 

It really is a good resource.  I went to work when I was 16 years old, all of this information would have been wasted on me at that time, between lack of interest and lack of applied experience.  It's been slower with work the last couple months so I've been focusing on learning about it to save my sanity and my liver.  This Neets paperwork really seems to explain things in a simple way that makes sense, and gets to the point. 

[HotBluePlates]

So, unless I misunderstand what I'm reading, the power ratings are always accumulative?
Eg:
...
1x8 ohm in parallel with 2x4 ohm in series=4 ohm@ 150 watts?

...

Help me out with a grade 10 physics question?

We can throw out the question of only 2 series resistors or 2 parallel resistors, as it seems "obvious" the individual power ratings will add.  But how do we figure out more complex scenarios?

This is why I linked NEETS, so you could read to get the basic Ohm's Law and Kirchoff's Law rules down.

     For Kirchoff, Parallel branches have the same voltage across each branch.  Total current is the sum of currents of each branch.

So now let's look at a simple case of 2 resistors in parallel to get an idea of how to tackle this question:

   1.  Draw the overall circuit.  Here, that's parallel 8Ω resistors with an AC Voltage Source.

   2.  Simplify to a single equivalent Total Resistance.  Here, R_total = 4Ω

What happens when we apply 100 watts?  How do the resistors split the power?

   3.  Calculate the Voltage required to deliver 100w into a 4Ω load.  We use Volts = √(Power x Resistance).

   4.  Calculate Total Current drawn by the load:  20v / 4Ω = 5A total

We notice that 20v x 5A = 100 watts.

Now we apply the fact that the voltage across each branch of a parallel circuit is the same (Kirchoff's Voltage Law):

   5.  Divide Branch Volts by Branch Resistance to find Branch Current:  20v / 8Ω = 2.5A

   6.  Calculate Power through the Branch Resistance:  20v x 2.5A = 50 watts

And we see that the 50w through each branch totals the 100 watts for the entire circuit.  The Total Circuit Current divided among the parallel branches in accordance with their individual resistances (same-resistance here, so we get same-current).


Open the image in a new tab (or save) to view larger.

[HotBluePlates]

So, unless I misunderstand what I'm reading, the power ratings are always accumulative?
Eg:
...
1x8 ohm in parallel with 2x4 ohm in series=4 ohm@ 150 watts?

...

Help me out with a grade 10 physics question?

Let's use the process above to figure out the more complex scenario:

   1.  Draw the overall circuit.  Here, one 8Ω resistor in parallel  with a branch made of two 4Ω resistors in series.

   2.  Simplify to a single equivalent Total Resistance.  An intermediate step is to combine the 4Ω resistors to an "8Ω equivalent resistor" that is in parallel with an actual 8Ω resistor.  Again, R_total = 4Ω

The Power changes to the assumed 150 watts delivered to the circuit:

   3.  Calculate the Voltage required to deliver 150w into a 4Ω load.  We use Volts = √(Power x Resistance) = 24.5 volts

   4.  Calculate Total Current drawn by the load (not drawn):  24.5v / 4Ω = 6.125A total

We notice that 24.5v x 6.125A = 150 watts.

We again apply the fact that the voltage across each branch of a parallel circuit is the same (Kirchoff's Voltage Law):

   5.  Divide Branch Volts by Branch Resistance to find Branch Current:  24.5v / 8Ω = 3.06A

   6.  Calculate Power through the Branch Resistance:  24.5v x 3.06A = 75 watts

And we see that the 75w through each branch totals the 150 watts for the entire circuit.

We calculate the power dissipated by each 4Ω resistor by knowing that the current through each 4Ω resistor is the current through that branch (3.06A, Kirchoff's Current Law)

   7.  Calculate 4Ω resistor Volts:  Current x Resistance = Volts --->  3.0625A x 4Ω = 12.25v per 4Ω resistor

   8.  Calculate Power dissipated by the 4Ω resistor:  12.25v x 3.0625A = 37.5 watts

We notice that 37.5 watts + 37.5 watts = 75 watts, so this branch dissipates the same total power as the other branch made of a single 8Ω resistor.  But that's only because the total resistance of each branch is the same.  If the branches were different-resistance, they would have different-current, and dissipate different-power.


Open the image in a new tab (or save) to view larger.

[AlNewman]

Thanks HBP.

You put a lot of time into explaining this, I really appreciate it.  It'll take me a few read overs to try and work it all out in my brain, plugging in different figures and such until I really get a grasp on it, but the information is all there and it's a huge help.

 The Kirchoff's law helps out a lot, how everything interacts in a circuit...I've been reading up on that the last couple days.  Also the formula to convert power to voltage without knowing the current has been a stumbling block.  I know I've seen that formula too, but probably glossed over it. 

Anyhow, you guys really provide a great service and wealth of information and don't get anywhere near enough credit for it but it is appreciated all the same.

[shooter]

have this printed out like 1ftX1ft hang it where you keep the pencils n paper, or save it to your desktop, comes in handy

[sluckey]

That wheel was around before I could spell electronics.     People with no basic algebra skills are usually amazed to know that every formula on that wheel is derived from E = I x R and P =E x I

[shooter]

 
I was in a 4 man "dorm" during NEET school, the other 3 had big boomed girl posters, I had the wheel 

[sluckey]

I had a 4" wheel 'sticker' on my little Craftsman toolbox.   

[AlNewman]

have this printed out like 1ftX1ft hang it where you keep the pencils n paper, or save it to your desktop, comes in handy

Thanks.  I've seen that many times, never saved it till now.  Most of the times people mention ohm's law, it's only in relation to voltage, current, and resistance, but power seems to get overlooked.  Understanding it as 4 seperate parts in unison makes a big difference.

I usually pick up things in life due to necessity.  People can talk theory all day long, and it goes in one ear and out the other, but it isn't until I have to put the theories into practice that I learn the nuts and bolts.  I never had any interest in being an engineer, but I would like to get the little pixies to dance on a copper string.

[PRR]

> ohm's law, it's only in relation to voltage, current, and resistance, but power seems to get overlooked.

German physicist Georg Ohm didn't speak of power. He did not have enough power to burn anything or to be billed for. (He apparently used an alcohol-lamp thermopile after he ran his voltaic battery flat.)

Today (even toward the end of Georg's life) we have systems where power matters. Do we need a dime part or a dollar part? Will it run-down a battery or run-up the electric bill? So the fourth term, Power, is usually needed in today's  practical problems even though it was not Georg's main problem.

[JPK]

Very nicely detailed answer HBP. Love the sketches and calc's.

[AlNewman]

> ohm's law, it's only in relation to voltage, current, and resistance, but power seems to get overlooked.

German physicist Georg Ohm didn't speak of power. He did not have enough power to burn anything or to be billed for. (He apparently used an alcohol-lamp thermopile after he ran his voltaic battery flat.)

Today (even toward the end of Georg's life) we have systems where power matters. Do we need a dime part or a dollar part? Will it run-down a battery or run-up the electric bill? So the fourth term, Power, is usually needed in today's  practical problems even though it was not Georg's main problem.

Well, I guess it's true that necessity breeds creation.
Power to me was the wattage sticker on the front of the amp in the music store until I decided that I'd like to tweak some components.  One thing led to another, and I figured I had better practice some due diligence in my tweaking before I burn my house down.  Also, if I feel comfortable knowing the limitations of the components I'm using I'll be able to do more and achieve a better result.

I had my computer playing youtube the other day, and a really good documentary came up about the history of electricity.  It must have been a mini series or something from tv that somebody edited together.  Anyhow, it was about 3 hours long, so I caught bits and pieces of it, but it got into how it evolved and recreated a lot of the experiments of different scientists through history.  Was a good find.

Actually here it is: