Series and Parallel Resistor question?

[shaneshane1]

Hi, i have drawn up 2 resistor examples, both have 15ohm totals! i was wanting to know what one would be the correct one to use or can i use anyone of them? "my" calculations tell me i can use anyone of them...

thanks...

 

[ericgibbs]

Hi, i have drawn up 2 resistor examples, both have 15ohm totals! i was wanting to know what one would be the correct one to use or can i use anyone of them? "my" calculations tell me i can use anyone of them...

thanks...

hi Shane.
Either would be OK.

NOTE: for a PCB layout the bottom one would be used to provide an solder point for all the resistors

 

[shaneshane1]

Thanks eric! the main reason i asked was because at tafe the teacher told use to make a series/parallel combination to form 15ohm 20W! he told me that the two parallel resistors in series (bottom picture) was incorrect? i just dont want to mention the topic to him until i am sure its right!

 

[Reloadron]

Thanks eric! the main reason i asked was because at tafe the teacher told use to make a series/parallel combination to form 15ohm 20W! he told me that the two parallel resistors in series (bottom picture) was incorrect? i just dont want to mention the topic to him until i am sure its right!

Ah, both of your drawings have the correct R Total, however, your initial post failed to mention what the teacher said about the power dissipation of the circuit. The teacher is correct in that the lower circuit will not dissipate 20 watts (only 10 watts) but the upper is correct for 20 watts. Look closely at your circuits.

Ron

 

[shaneshane1]

Ah, both of your drawings have the correct R Total, however, your initial post failed to mention what the teacher said about the power dissipation of the circuit. The teacher is correct in that the lower circuit will not dissipate 20 watts (only 10 watts) but the upper is correct for 20 watts. Look closely at your circuits.

Ron

isnt it the same thing? the top circuit produces the same current and wattage as the bottom circuit, the top two series (in the top picture) resistors have 500mA running through them and the same for the two under them, so 1Amp total draw...

So whats the bottom circuit doing?

 

[MRCecil]

Ah, both of your drawings have the correct R Total, however, your initial post failed to mention what the teacher said about the power dissipation of the circuit. The teacher is correct in that the lower circuit will not dissipate 20 watts (only 10 watts) but the upper is correct for 20 watts. Look closely at your circuits.

Ron

Actually, both circuits are identical save the useless jumper in the lower version presented. In the lower circuit, there is no current through the jumper given the potential difference at that point in both legs is 0.000...0V considering/assuming all resistors are absolutely 15 ohms out to many 0's. Therefore, the current through all resistors is equal in both cases. If the current and resistance are equal in both cases, the power dissipation must be equal in both cases for all resistors. The student's instructor appears to be in error.

 

[shaneshane1]

Actually, both circuits are identical save the useless jumper in the lower version presented. In the lower circuit, there is no current through the jumper given the potential difference at that point in both legs is 0.000...0V considering/assuming all resistors are absolutely 15 ohms out to many 0's. Therefore, the current through all resistors is equal in both cases. If the current and resistance are equal in both cases, the power dissipation must be equal in both cases for all resistors. The student's instructor appears to be in error.

But the bottom circuit becomes basically two 7.5ohm resistors in series at a 5watt rating each resistor, so that would mean that two 15ohm resistors in parallel would effectivly have a power rating of 10watts 7.5ohm? i think i am starting to understand what the teacher means.... because the two 15ohm parallel resistors basically = one 10watt 7.5ohm resistor, and two of them in series (the bottom circuit) cant get any higher than 10 watts because they are in series?
now that i have had everyones help i understand it better now... the teacher didnt say "why" i was wrong! so i started to question what i thought i already new... So now i know why i was wrong,

One circuit "allows" up to 20watts and the other "allows" up to 10watts? am i right in saying that the second circuit (the bottom one) is drawing 5watts more that its "rated" to draw?

 

[MRCecil]

But the bottom circuit becomes basically two 7.5ohm resistors in series at a 5watt rating each resistor, so that would mean that two 15ohm resistors in parallel would effectivly have a power rating of 10watts 7.5ohm?

Can you calculate the current through the jumper? How much current can one expect if the potential is exactly the same at both ends of that jumper. Place a 1 ohm resistor in place of that jumper and calculate the current. Again, if the potential is exactly the same on both ends of that 1 ohm resistor how much current will flow through that 1 ohm resistor. Run the numbers!

i think i am starting to understand what the teacher means.... because the two 15ohm parallel resistors basically = one 10watt 7.5ohm resistor, and two of them in series (the bottom circuit) cant get any higher than 10 watts because they are in series?
now that i have had everyones help i understand it better now... the teacher didnt say "why" i was wrong! so i started to question what i thought i already new... So now i know why i was wrong,

One circuit "allows" up to 20watts and the other "allows" up to 10watts? am i right in saying that the second circuit (the bottom one) is drawing 5watts more that its "rated" to draw?

Run the numbers and present them to your instructor in a diplomatic manner. Consider the ENTIRE circuit and the parameters given!

Two 15 ohm resistors in parallel dropping 7.5V equates to a total current of 1A; 0.5A through each 15 ohm resistor. The second pair do the same...identical sections. The total resistance is 15 ohms with It=1A. That comes to a total circuit dissipation of 15W. Without the jumper, the result is EXACTLY THE SAME... 1A, 15V, 15 ohms & 15W. The circuits are identical electrically.

Now if you were actually tasked to produce a circuit with Rt=15 ohms with a total power dissipation of 20W vice 15W, then both you and your instructor are in error as neither circuit fits the parameters. Both circuits you presented above yield an Rt of 15 ohms. But the voltage is wrong... it should be 17.32V to produce a total of 20W circuit dissipation and not 15V.

 

[Diver300]

because the two 15ohm parallel resistors basically = one 10watt 7.5ohm resistor, and two of them in series (the bottom circuit) cant get any higher than 10 watts because they are in series?

That is where your error is.

Two resistors in series have the same current. If each resistor is rated at 10 W, 7.5 ohms then they have a rated current of 1.15 A. Put the resistors in series, and that current doesn't change, you can only get 1.15 A though the pair without risk of damage.

However, the two resistors in series have twice the voltage drop, so with the same current, there is twice the power dissipated.

I think that there is a simpler way of looking at this. If one (of the original 5W) resistors can convert 5W of electrical power into heat without overheating, then four of them can convert 20W. The electrical circuit has to be symmetrical so that all four are in equivalent positions, and both of your example circuits are.

(It is also important that the electrical circuit is stable, but with simple resistors it will always be stable. However, a flip-flop circuit is symmetrical but not stable when the current in both load resistors is the same. It will end up with all the current in one load resistor).

 

[shaneshane1]

That is where your error is.

Two resistors in series have the same current. If each resistor is rated at 10 W, 7.5 ohms then they have a rated current of 1.15 A. Put the resistors in series, and that current doesn't change, you can only get 1.15 A though the pair without risk of damage.

However, the two resistors in series have twice the voltage drop, so with the same current, there is twice the power dissipated.

I think that there is a simpler way of looking at this. If one (of the original 5W) resistors can convert 5W of electrical power into heat without overheating, then four of them can convert 20W. The electrical circuit has to be symmetrical so that all four are in equivalent positions, and both of your example circuits are.

(It is also important that the electrical circuit is stable, but with simple resistors it will always be stable. However, a flip-flop circuit is symmetrical but not stable when the current in both load resistors is the same. It will end up with all the current in one load resistor).

So is the parallel resistors in series (bottom circuit) equal to a 15ohm 20watt resistor?

 

[MrAl]

Hello,


Another way of looking at this is how much power does the resistor set draw from the power supply of 15v?
Since we know the source is 15v, if we know the current draw we can calculate the total power used by the resistors.

In the top picture, the total resistance is 15 ohms, and that means the top set draws 1 amp which means the source supplies 15 watts.
In the bottom picture, the total resistance is 15 ohms and that means the bottom set also draws 1 amp which means the source still supplies 15 watts.

Both circuits draw the same amount of current from a constant source voltage so they both dissipate the same power.

BTW, the short does nothing to change the circuit because it effectively jumpers two potentials that are EXACTLY the same for ALL time.

The only other way to look at this is from a statistical standpoint, where each resistor can be off by a certain tolerance like 10 percent. Given a random difference in each resistor, which set comes up statistically closer to 15 ohms total, or do they both come up the same anyway? See if you can figure this out
(Note that if each resistor can be off by a random amount up to 10 percent off, applying the short might then have an effect. If this were a real life circuit we might think about this too).

 

[shaneshane1]

Hello,


Another way of looking at this is how much power does the resistor set draw from the power supply of 15v?
Since we know the source is 15v, if we know the current draw we can calculate the total power used by the resistors.

In the top picture, the total resistance is 15 ohms, and that means the top set draws 1 amp which means the source supplies 15 watts.
In the bottom picture, the total resistance is 15 ohms and that means the bottom set also draws 1 amp which means the source still supplies 15 watts.

Both circuits draw the same amount of current from a constant source voltage so they both dissipate the same power.

BTW, the short does nothing to change the circuit because it effectively jumpers two potentials that are EXACTLY the same for ALL time.

The only other way to look at this is from a statistical standpoint, where each resistor can be off by a certain tolerance like 10 percent. Given a random difference in each resistor, which set comes up statistically closer to 15 ohms total, or do they both come up the same anyway? See if you can figure this out
(Note that if each resistor can be off by a random amount up to 10 percent off, applying the short might then have an effect. If this were a real life circuit we might think about this too).

Thanks... so if all resistors in the bottom circuit are for theory sake the EXACT same ohms (15 exactly) then the "jumper" will do absolutley nothing? meaning that i am not wrong? in theory!

 

[ericgibbs]

Hi Shane,
Like I said, both the same.

If the tolerances of the resistors are not given in the question, I would always assume precision values.

 

[Reloadron]

I think what the instructor / teacher is looking at or wanting you to see is equivalent circuit. You may want to ask him about that. Let's see what he says and hear his explanation. The upper circuit is two series circuits in parallel and the lower circuit is two parallel circuits in series. No, you aren't wrong in theory as the circuits are the same. However, I don't think that is how the teacher sees it or what he wants. Anyway, I based my first reply on what I think he was getting at when he said your lower circuit was incorrect.

Ron

 

[MrAl]

Thanks... so if all resistors in the bottom circuit are for theory sake the EXACT same ohms (15 exactly) then the "jumper" will do absolutley nothing? meaning that i am not wrong? in theory!

Hello again,


Yes, i agree with both Eric and Ron. In fact, if i remember right in circuit theory if two nodes have the exact same voltage for all time then they can be considered one single node, which of course means that connecting them together has no effect on the circuit. This may not always work with circuits that are not considered to be "lumped", but this circuit is so it definitely works here.

Another example of something like this is the so-called "virtual ground" of an op amp. In some theory the inverting terminal is considered to be equal in potential to the non inverting terminal even though they are not connected, and this leads to simplifications too.

Statistically given a tolerance of max plus or max minus the top circuit has much more of a chance of being closer to 15 ohms than the bottom circuit but some cases are rather close, and as others have said the teacher probably isnt looking for this anyway. This is rather interesting however, in that in a real life circuit sometimes shorting those two points will lead to a total resistance closer to 15 ohms than not shorting it, or vice versa, depending on which of the resistors are off and how much they are off by and in what direction they are off.
Another interesting statistic is that four resistors connected this way have more of a chance of being close to 15 ohms than any single resistor. Stated another way, two resistors connected in series will have a resistance closer to the package stamped value on average because the only way they can be as far off as either one alone is if they are both off the same amount and in the same direction! Pretty interesting i think. The min and max will be the same of course, but on average the two will be better.

 

[shaneshane1]

Well... re-asked the tafe teacher about the resistor circuit this week... turns out i was right! and he was wrong! took 2 teachers to see the facts... not a good sign seeing that the next subject is AC theory.