Parallel resistors

[jeff304]

Can any one think of a real-world application where a resistor of 100K or greater would be required to be run in parallel with other resistors?

I have designed a calculator using C++ that returns the value of the smallest resistor when a resistor of 100K or greater is included in the circuit. According to Ugly's Reference, the Rt should be less than the value of the smallest resistor.

 

[charlie b]

Re: Parallel resistors

I am afraid that I do not quite understand the question. It is true that a set of parallel resistors will have an effective, total resistance (Rt) that is less than the smallest resistance in the set. However, if there is a vast difference between the values of resistances, such as placing a 2 ohm in parallel with a 100,000 ohm, then the Rt will be very close to the smallest value. In this case, the correct answer is 1.99996 ohms, and a calculator might just round that answer back up to 2 ohms.

As to real world applications, I do not generally deal with resistors as single components. But I do know that voltmeters that are permanently installed in switchboards will have very high input resistances that are in parallel with the bus.

 

[dereckbc]

Re: Parallel resistors

Yes it is possible. In electronic equipment design there are circumstances where you need a resistance value that is not a standard value such as attenuators.

 

[mikeackley]

Re: Parallel resistors

Jeff:

I'm not sure how specific of an example you might be looking for but I can think of many occasions (100's + perhaps) in which a circuit designer might need to run one or more resistors in parallel with another of 100k or more. Voltage regulation, controlling the charging/discharging of capacitors, and timing circuits just to name a few. Or as far as that goes, any circuit requiring a specific resistance that is not readly available in a single resistor. Simple case would be a circuit requiring a resistance close to 70k ohms...try buying one of those. Instead run a 220k ohm and a 100k ohm resistor in parallel and you've got it.

Let me take a checkpoint with you here, Is this what you are looking for?

The more I think about it, if you have designed a calculator, you probably had to run resistors > 100k ohms in parallel in its circuitry, so I'm probably misreading your question.

[ February 24, 2003, 03:49 PM: Message edited by: mikeackley ]

 

[jeff304]

Re: Parallel resistors

Thanks for the replies, guys!

I think all of you answered my question to my satisfaction.

Just to clarify the question; I am writing a suite of software targeted at persons in any trade that have to make electrical calculations with some degree of accuracy.

My question was basically; How accurate does this program have to be to serve the needs the people making these calculations?

Before reading your replies, my program would give a result to the nearest 1/100,000th, being accurate only to 1/10,000th.

After reading your replies, I gather there may actually be an instance where more accuracy is needed. I went back into my program and changed the the source code to give an answer to the nearest 1/10,000,000,000th, meaning it is now accurate to 1/1,000,000,000th of an ohm.

Knowing from first-hand experience how tedious figuring three or more parallel resistors manually is, I designed this program to figure an almost unlimited number of parallel resistors, simply by choosing the number of resistors in the circuit, entering the values of each resistor and clicking the "calculate" button. (I believe the code I am using would limit the program to 80 decimal places).

Just out of curiosity I ran the examples given through my program and came up with the following: 2 ohms parallel with 100,000 ohms came out to be; 1.9999600008 ohms, 220k with 100k came out to be; 68.750k, very close to the required 70k.

I am very thankful to Mike Holt for providing this forum where technical questions are answered by seemingly, very knowledgable and experienced people.

 

[Len_B]

Re: Parallel resistors

...I went back into my program and changed the the source code to give an answer to the nearest 1/10,000,000,000th, meaning it is now accurate to 1/1,000,000,000th of an ohm...

Jeff,

Just wondering... accurate to 1/1,000,000,000 ohm ?
How would you measure resistance and achieve an accuracy of 9 significant digits---especially in the field? I'm just skeptical that numbers spanning 9 orders of magnitude have much meaning past the first 4 or 5 digits (possible exception a very high tech controlled laboratory environment).

Len

 

[jeff304]

Re: Parallel resistors

Len, glad to hear from you.

To possibly answer your question:

"Just wondering... accurate to 1/1,000,000,000 ohm ?
How would you measure resistance and achieve an accuracy of 9 significant digits---especially in the field?"

I have aquired a taste for programming. My goal is to write useful programs to run from a computer. At this stage, this particular portion of my program only calculates the Rt for multiple resistors in parallel with known values. Your question has prompted me to edit this portion of my program to provide a person in the field the ability to take an ohm reading, compare it to the resistance required by the circuit, run the numbers through the program and determine which resistor has dropped out.

Of course, if one can isolate each resistor from the circuit, the one that has dropped out can be found manually, if you are dealing with a solid state board, it may be easier to replace the board.

At any rate, I am hoping that people dealing with electrical circuits will find my software useful and accurate, it may be overkill for some, others may find it a must-have(hopefully).

I most certainly appreciate the feed-back, it has put a new twist on this portion of my program that did not occur to me.

 

[mikeackley]

Re: Parallel resistors

jeff:

Will this calculator also work "Backwards"? A real Plus ++. Using the previous simple example where you want to end up with 70K ohms: Designer/User starts out by keying in the resultant figure = 70K; Second, User keys in a "what if" starting value, lets say 100K, then the calculator returns a display of what else is needed in parallel, i.e., slightly more that 220K. User chooses 220K with the remainder adjusted for (if necessary) by placing another resistor(s) in series with the rest, or perhaps another set of parallel resistors in series with the first set.

 

[charlie b]

Re: Parallel resistors

All the great advances in the sciences started with new people looking at old problems in new ways. I would not, for the world, discourage innovative thinking. But there is a concept that I would like to be sure you understand, lest you accidentally conclude that your program can do more than it is, in fact, capable of doing. Len’s question was along the same lines. I will try to be more clear.

The concept revolves around the difference between “precision” and “accuracy.” Precision has to do with significant digits (Len’s question), and with the units with which you make your measurements. To use a foot-long stick to measure the width of a room is more precise than using a yard-long stick. Measuring in units of inches is more precise, and units of millimeters is still more precise. On the other hand, accuracy has to do only with whether the measurement is right.

The relevant rule is that the results of a calculation can be no more precise than the degree of precision of any of the input values. That is, if you can’t measure the resistance of each parallel resistor to a precision level of 9 significant digits, then it is inaccurate to present the results (Rt) to 9 significant digits.

Here’s a simple example. Let R1 be a 10 ohm resistor with a manufacturing tolerance of 10%. Its actual value could then be anywhere from 9 to 11 ohms. Let R2 be a 3 ohm resistor with a manufacturing tolerance of 5%. Its actual value could then be anywhere from 2.85 to 3.15 ohms. Place R1 and R2 in parallel, and run your program. To 9 significant digits, your answer would be 2.307692308. However, given the range of manufacturer’s tolerances, the true (i.e., accurate) answer could be anywhere from 2.16455696 to 2.448763251.

 

[mikeackley]

Re: Parallel resistors

Charlie:

Excellent point and very well stated. However (and this is in no way a rebuttal or debate of anything you or Len have posted), there certainly are instances in which the level of measurement needed is satisfied with single units of ohms, just as there are instances in which measurements of 100,000 ohms (or more) are necessary. Now if the real question that started this Post is simply one of rounding, anything to add to what you or Len have stated would be redundant. On the other hand, if Jeff's original question is really whether or not a calculator should be able to apply simple mathematical calculatons on numbers equal to or greater than 10 to the 5th power, isn't that something quite different? I'm still not sure which is the case, but all of us probably have better things to do than pound on this one anymore.

[ March 05, 2003, 10:35 AM: Message edited by: mikeackley ]

 

[jeff304]

Re: Parallel resistors

Hi guys, I'm back.

So many variables, my head is spinning.

In my reply to Len, I stated in a round-about way that he has given me the idea to modify the program to run backwards.

Better stated; Mikeackley asks: "Will this calculator also work "Backwards"? A real Plus ++. Using the previous simple example where you want to end up with 70K ohms: Designer/User starts out by keying in the resultant figure = 70K; Second, User keys in a "what if" starting value, lets say 100K, then the calculator returns a display of what else is needed in parallel, i.e., slightly more that 220K. User chooses 220K with the remainder adjusted for (if necessary) by placing another resistor(s) in series with the rest, or perhaps another set of parallel resistors in series with the first set".

The answer is yes, that is the modification I was talking about.

Charlie B, I don't quite understand the example of yardsticks, inches, etc. Mathematically speaking, if a calculation is carried out to 10 places behind the decimal, then it is only accurate to 9 places behind the decimal because the 10th place is either rounded up or down. The example you gave came out to be 2.3076923077 when I ran it through my program. You raised another question in my mind; taking a group of resistors at face value, ignoring the manufacturers tolerance and calculating Rt, isn't it possible the answer generated by my program could be completely out of the allowable tolerance range for the circuit being designed? I almost feel that I should be pushing a broom for a living.

I really hope you guys don't think we are beating a dead horse, I have gained a little bit more insight into what would be needed to be of practical use to people in the trade.

I shall now crawl back into my programming software and begin the daunting task of making the program run forward AND bakcward.

Once completed, maybe some of you would be interested in an evaluation copy to see if it is of any practical use. (Virus-free, I guarantee)
Jeff

 

[charlie b]

Re: Parallel resistors

Originally posted by jeff304:I don't quite understand the example of yardsticks, inches, etc.

If you are calculating the service load of a new residence, you start with watts per square foot for lighting. For this purpose, it is good enough to state the building’s length and width to the nearest foot. But if you are buying carpet for a bedroom, you must measure the room to the nearest inch, or the carpet might not fit. If you are installing a new countertop for the kitchen, you must measure the width of the wall to the nearest 1/4 inch. But a measurement to plus or minus 1/4 inch would not be good enough, if your doctor is performing surgery on your eye. This is what I meant by “precision.”

My point was that the results of a calculation cannot be more precise than the input information. If you can only measure resistance values within 10%, or even within 0.01%, then it is nonsense to quote an Rt to 9 decimal places.

 

[dereckbc]

Re: Parallel resistors

Jeff, hang in there. It is good to experiment. You will learn something. I hold a 1st class radiotelephone license, and an amateur general class license, so I am familiar with electronic circuit design. So here is a piece of advise as of how far to take the accuracy of your calculator.

In design we measure with a micrometer, mark it with chalk, and cut it with an axe. Standard resistors come in 5%, 10%, and 20% ratings. There are precision resistors that come in 1% tolerance.

Good Luck

DC

 

[jeff304]

Re: Parallel resistors

It took DAZE, but I found the equation to find the missing resistor value. It took about ten minutes to code and compile a rough draft of this portion of the program.

Using the example given; r1=220, r2=100 ohms, run through the first portion of the program comes out to 68.75 ohms Rt.

Now, say we need 220 ohms total. In the second portion, we key in 68.75 ohms as the existing value, next key in the needed value of 220, the program spits out 100 ohms required to satisfy the need for 220 ohms.

At: http://www.rfcafe.com/references/electrical/resistor_values.htm, I found a listing of common resistor values with variances of 1,5 and 10%.

dereckbc posted that some resistors come in 20% tolerance values, does anyone have a link to such a listing or table?

Also, to clear up some confusion; at: http://www.engplanet.com/content/resistorinfo.html, I see that a white band would indicate a multiplier of 10^9, or 1,000,000,000. So, to answer my own question, yes my program needs to accurate/precise (the terms are synonymous) to ten decimal places.

 

[hurk27]

Re: Parallel resistors

Just for thought another good use for a program would be to caculate how many resistors you would need in a circuit to dissapate lets say 100 watts at 50 ohms. now if we use 10 watt resistors it would take 10 of them or more if you didnt want them to run hot 10x50=500 ohms per resistor.

 

[jtb]

Re: Parallel resistors

Suggestions for further development!

Enter the tolerance of resistors and power handling. You can then calculate resistance values typical and the tolerances of real world resistors and other goodies, like heat dissipated, etc.

Example: Input 100KOhm resistor, +/- 10% tolerance

Program calculates for 100Kohm, 90Kohm, 110KOhm
Typical is 100Kohm, Min is 90Kohm, Max is 110Kohm.

In calculations with several resistors, run all variations, and get typical, lowest and highest values possible, or typical and +/- range tolerance for combo.