Flummoxed by a basic parallel resistance question

[Charlie_Don't_Surf]

I normally bash through these worksheets quite quickly (or at least, I rarely get one like this which I just can't suss out), but this one has got me stumped.

Yes, I've googled it and youtubed it for a while (although usually I only really resort to that when I don't have the knowledge to work it out myself, or when logical deduction can't crack it) but I can't find anything which addresses this exact situation.

So I know that 1/Rt = 1/R1 + 1/R2 + 1/R3, and then you'd need to convert 1/Rt into a decimal to get your answer. but I don't know how to do the reverse operation, with the limited information provided here.

So there's no values for the voltage or current (which I guess you could 'make them up' in an attempt to use ohms law as a roundabout way of getting the answer, but I'm sure that's not the way we're supposed to approach this question, or even whether that would necessarily work).

Maybe I've missed something really obvious, and if so I risk looking like a plum here, but whatever, if I learn from it then it was worth it.
I have a suspicion that it would be possible to transpose a formula to work it out, but I'm not sure how to formulate the formula. I guess one such formula might be 1/R3 = 15Ohms - (1/48 + 1/80), but then that's not right, I dont think so anyway, cause the 15 ohms needs to be converted back into 1/something. That's where I'm stuck.

1/48 and 1/80 are not difficult to calculate, but I don't see how that helps. Basically, it seems that the problem needs to be addressed from the other end, i.e. I need to know what to do to the 15 ohms to make it equal 1/something. From trial and error I find that 1/0.065 = 15.3846, but in an exam (or eventually on a job) I can't waste time on trial and error, which anyway would only reach an approximate answer. Real life won't have multiple answers from which I can choose the closest one eh.

So basically, could someone kindly advise me as to the best/simplest way to convert 15 into 1/something.

Cheers

 

[Lister1987]

Reverse it? 1/15 (1 divide by 15) gives 0.06666666667 (note that the known resistances have been divided by 1, it would make sense therefore for the 15 to be divided by 1, giving the 0.066 you've already alluded to

 

[Lucien Nunes]

The reciprocals of resistances are conductances. G=1/R and R=1/G.
You can add and subtract conductances in parallel just like resistances in series.
With three conductances in parallel, the two known ones and the unknown, you can write:
G3 = Gtotal - G1 - G2.
And therefore the same will apply to the reciprocals of the resistances. Substitute 1/R for G
1/R3 = 1/Rtotal - 1/R1 - 1/R2
And rearrange for R3
R3 = 1/ (1/Rtotal - 1/R1 - 1/R2)

 

[Charlie_Don't_Surf]

Reverse it? 1/15 (1 divide by 15) gives 0.06666666667 (note that the known resistances have been divided by 1, it would make sense therefore for the 15 to be divided by 1, giving the 0.066 you've already alluded to

Thank you. So simple I can't believe I overlooked this. Thanks for the explanation, of course, it makes sense.

 

[Charlie_Don't_Surf]

The reciprocals of resistances are conductances. G=1/R and R=1/G.
You can add and subtract conductances in parallel just like resistances in series.
With three conductances in parallel, the two known ones and the unknown, you can write:
G3 = Gtotal - G1 - G2.
And therefore the same will apply to the reciprocals of the resistances. Substitute 1/R for G
1/R3 = 1/Rtotal - 1/R1 - 1/R2
And rearrange for R3
R3 = 1/ (1/Rtotal - 1/R1 - 1/R2)

Thank you for this detailed reply/solution.
With the first one there, G3 = Gtotal - G1 - G2, surely though, we don't know the conductance values of G1 or G2? Perhaps I'm missing something. But the relationship between conductance and resistance is interesting thank you for sharing this. I will try and remember that about being able to add conductances in parallel, I'm sure that will come in handy at some point

Regards this bit:

"And therefore the same will apply to the reciprocals of the resistances. Substitute 1/R for G
1/R3 = 1/Rtotal - 1/R1 - 1/R2
And rearrange for R3
R3 = 1/ (1/Rtotal - 1/R1 - 1/R2)"

I don't really follow. I'm not asking for you to try harder to explain it if you don't want to/can't make it any clearer, I'm sure with time and more learning, I'll look back and understand this in the context of more learning. Maths was never my strongest subject to be honest, and although I do get good exam grades, I have to work hard sometimes to make sense of new maths concepts.

The bit:
1/R3 = 1/Rtotal - 1/R1 - 1/R2
And rearrange for R3
R3 = 1/ (1/Rtotal - 1/R1 - 1/R2)

It looks like you've transposed the formula in a way which I hadn't thought of. Although from what I was taught / have read, arent you supposed to reverse the operation if you move something to the other side of a formula, i.e.

1/R3 = 1/Rtotal - 1/R1 - 1/R2
If we were to try to isolate R3 on the one side of the formula, surely then we'd have to move the 1 over to the other side of the formula, but multiply the rest of that side of the formula by 1? But then surely that wouldn't have any effect on the other side of the formula, because 1(1/Rtotal - 1/R1 - 1/R2) would just be the same as 1/Rtotal - 1/R1 - 1/R2

Thank you for your reply, it has certainly got me thinking