# Missing parallel resistor value

#### ryancousins

Joined Jul 15, 2012
14
I have searched the forums and the tutorials and have not found an answer to my question. I am looking for the value of an unknown resistor, given the remaining value(s) of resistors, and the total value. I have seen derivations of the "product over sum" formula, however, I would like to use the generic "reciprocal" formula that applies to more than 2 resistors at a time.

So I'd like to solve for $$R_x$$ in the standard "reciprocal" formula, where $$R_x$$ represents the value of the unknown resistor, and $$R_t$$ represents the total resistance of the circuit:

$$R_t=\frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_x}}$$

I have seen the following as a derivation that solves for $$R_x$$...

$$R_x=\frac{1}{\frac{1}{R_t}-\frac{1}{R_2}-\frac{1}{R_3}$$

If this is accurate, then can someone show me the algebraic manipulation to get to it from the original?

Thanks!

#### shteii01

Joined Feb 19, 2010
4,644
Seriously? Isn't that 7th or 8th grade mathematics?

#### studiot

Joined Nov 9, 2007
4,998
Seriously? Isn't that 7th or 8th grade mathematics?
This is homework help and we do not look down on those who are perhaps meeting things for the first time.

ryan, please post your actual question rather than some formula that may or may not be applicable. We can take it that post1 included your necessary attempt for help.

This does not mean that we will do your problem for you, just that we will try to provide proper help and guidance towards your own solution.

#### The Electrician

Joined Oct 9, 2007
2,866
The OP has only posted one other time, a while ago. I think this is not really homework, but a work related problem.

#### ryancousins

Joined Jul 15, 2012
14
shteii01:

1. I don't see how your response was relevant or helpful in any way. The least you could have done is offer assistance after you belittled me.

2. I can assure you that the manipulation of the formula is not in the 7th or 8th grade math curriculum. I can send you a link to the Common Core State Standards for Mathematics, if you wish. I help middle-school students with math, so I know the curriculum in detail. I worked out my question. I obviously just had a brain fart. I understand the algebraic rules of associativity, commutativity, identity, etc., and I have taken Calc I, Calc II, and Linear Algebra, so I have at least a basic understanding of math.

Everyone else: I apologize if I posted in the wrong forum. I was asking about this for some homework problems. I didn't want to post a specific problem. I wanted to post the generic formula so I could apply it to all problems. In the future I will post these type of questions in a different forum. What forum would be a more appropriate location for non-specific homework-problem questions?

#### JoeJester

Joined Apr 26, 2005
4,390
Ryan,

You can confirm your question by doing the math. Take three resistors in parallel, values are 100, 200, and 300. Compute Rt. Then use the second formula and calculate the resistance of one of the resistors.

Look at the formula closely.

Joined Apr 30, 2011
1,581
What forum would be a more appropriate location for non-specific homework-problem questions?
We have a math forum.

#### shteii01

Joined Feb 19, 2010
4,644
shteii01:

1. I don't see how your response was relevant or helpful in any way. The least you could have done is offer assistance after you belittled me.

2. I can assure you that the manipulation of the formula is not in the 7th or 8th grade math curriculum. I can send you a link to the Common Core State Standards for Mathematics, if you wish. I help middle-school students with math, so I know the curriculum in detail. I worked out my question. I obviously just had a brain fart. I understand the algebraic rules of associativity, commutativity, identity, etc., and I have taken Calc I, Calc II, and Linear Algebra, so I have at least a basic understanding of math.

Everyone else: I apologize if I posted in the wrong forum. I was asking about this for some homework problems. I didn't want to post a specific problem. I wanted to post the generic formula so I could apply it to all problems. In the future I will post these type of questions in a different forum. What forum would be a more appropriate location for non-specific homework-problem questions?
Took me less than 10 minutes.

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#### The Electrician

Joined Oct 9, 2007
2,866
Sometimes it's better to approach a circuit considering the elements as admittances rather than impedances.

If you re-formulate your last equation like this: you can see a quick way to solve the problem with a handheld calculator. Do it like this if you use an HP calculator with a stack:

Type in total resistance Rt and press the 1/x key; this converts the resistance to a conductance (same as admittance for resistors). Now type the value of the first resistor, R1; press the 1/x key and then the - key. You have subtracted the conductance of R1 from the conductance of Rt. Type in the next resistor value, R2; press the 1/x key and then the - key. You have now subtracted the conductance of R2 from the running calculation.

Keep doing this until you have entered the last resistor, Rn. Now press the 1/x key; you have the value of Rx in the display.

On a non-HP calculator, enter Rt and press the 1/x key. Now, one at a time, subtract the reciprocal of R1, R2...Rn from the running calculation. At the end, press the 1/x key and see Rx in the display.

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• MrChips

#### WBahn

Joined Mar 31, 2012
26,398
Seriously? Isn't that 7th or 8th grade mathematics?
And what if the OP is in 6th grade?

Or has been out of school for 40 years?

We can (and usually are) a bit harsh when people don't show their work (especially on a repeated basis), but we seldom get harsh about the quality of that work except in the context of making specific points about how to improve it.

#### WBahn

Joined Mar 31, 2012
26,398
2. I can assure you that the manipulation of the formula is not in the 7th or 8th grade math curriculum.
Boy, then the standards have definitely plummeted more than I thought in the last 35 years or so. I remember starting into this kind of stuff in 6th grade and being into it big time in 8th. For whatever reason, I don't have a strong recollection of what we covered in 7th grade, but I do recall doing stuff involving manipulating fractions and so we definitely covered things like 1/(1/x) = x.

So

$$R_t = \frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_x}} \ \ \frac{1}{R_t} = \frac{1}{ \frac{1}{ \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_x} } } \ \ \frac{1}{R_t} = \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_x}$$

Note that this last equation is usually the form given for the case of multiple resistors in parallel.

From here is it a matter of subtracting things from both sides, which I do recall covering at the very beginning of 8th grade algebra.

$$\frac{1}{R_t} - \frac{1}{R_1} - \frac{1}{R_2} = \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_x} - \frac{1}{R_1} - \frac{1}{R_2} \ \ \frac{1}{R_x} = \frac{1}{R_t} - \frac{1}{R_1} - \frac{1}{R_2}$$

And then it's that same 1/(1/x) rule from 6th grade again.

$$\frac{1}{\frac{1}{R_x}} = \frac{1}{ \frac{1}{R_t}-\frac{1}{R_1}-\frac{1}{R_2} } \ \ R_x = \frac{1}{ \frac{1}{R_t}-\frac{1}{R_1}-\frac{1}{R_2} }$$

So I don't think I buy the claim that this is beyond 7th or 8th grade math -- unless it really has dropped significantly (which I won't place any bets against).

I can send you a link to the Common Core State Standards for Mathematics, if you wish.
Could you? I'd actually be interested in them. Yeah, I could look them up myself without much difficulty (and looking up the Colorado standards would probably be more useful to me), but since you offered....

I worked out my question. I obviously just had a brain fart.
Happens to all of us.

Everyone else: I apologize if I posted in the wrong forum. I was asking about this for some homework problems. I didn't want to post a specific problem. I wanted to post the generic formula so I could apply it to all problems. In the future I will post these type of questions in a different forum. What forum would be a more appropriate location for non-specific homework-problem questions?
This is not an unreasonable forum to post them to. It can really help if you provide some more context about the question, particularly when it isn't a specific homework problem.

There is also a Math forum which might be a bit better when the question is truly math related.

• anhnha

#### WBahn

Joined Mar 31, 2012
26,398
So, I didn't realize that the "Common Core State Standards for Mathematics" was a national-level effort. I assumed that "state standards" implied something at the state level. Silly me.

So I was looking (just at the Wikipedia article) and one of the specific content items it mentioned was that by the end of Grade 2 students are supposed to be able to be able to add any two one-digit numbers from memory.

My daughter -- who if she were just a week younger would have just started kindergarten but instead just started first grade -- was expected to enter first grade being able to do this. As it was, by the end of the summer we had her doing pretty well on numbers up to 20+10 (as long as one of the numbers was 10 or less she could do it) and 20+20 if she got to use beads or pencil/paper. Whe was starting in on subtraction but definitely struggling with the concept a bit. Now, just six weeks into first grade, she is really getting the hang of subtraction involving numbers up to 20.

And she is not at the head of her class, which is to be expected since she is all but a year younger than many of her classmates, which makes a huge difference at age six.

So if the national standards are only expecting students to do by the end of second grade what my daughter was doing at the beginning of first (and given that she was only a hair's breadth away from being at the beginning of kindergarten), then I guess it's not surprising at all that they've removed all semblence of algebra out of 7th and 8th grade.

Reminds me of the school district where I was in kindergarten. My dad and I ran across some of the "outcomes" that my mom had put into a scrapbook and children weren't expected to even know the entire alphabet until sometime in second grade. That was the final straw for my parents and so we moved to a district where the students were reading in kindergarten (and I got to play catch-up).

My daughter's school teaches cursive before print and my daughter could write in cursive, upper and lower case, before she finished kindergarten (and her cursive is better than mine ever was). Now many school districts have formally eliminated it from the curriculum altogether.

We are almost certainly going to have to move and take her out of this school, which is a real shame. We haven't found anything like it in the area we will be in.

#### MrChips

Joined Oct 2, 2009
24,643
I like The_Electrician's idea of simply summing admittance. The math is simple and straight forward.