Math Symbol Mystery

October 25, 2009 8:19 PM

I've never seen this mathematical symbol used this way before. Can anyone tell me what it means?

Ok, my ignorance is on display for the world to see…

Please look at this image .

I'm referring to the parallel bars between the two resistances at the top. Obviously anyone who's taken 9th grade geometry knows that it is a symbol for describing a relationship as being parallel. But how does it fit here? How is it used to derive the final value of the voltage gain (3.82)?

posted by mazniak to education (8 comments total)

It means those resistors are in parallel, so it's 1/1000 + 1/680 = 1/R. Or to simplify, (1000*680)/(1000+680).
posted by DMan at 8:23 PM on October 25 [1 favorite]

It means the resistors are in parallel. 1 / ( (1/1k) + (1/680) ) = 405.
posted by fritley at 8:24 PM on October 25 [1 favorite]

Probably it means two resistances in parallel where R=1/((1/R1)+(1/R2)).

I've never seen it written like this before either, but calculating parallel resistance is a fairly common thing so it's not such a huge leap.
posted by GuyZero at 8:24 PM on October 25 [1 favorite]

Wow AskMeFi, you guys rock. Thanks so much for the quick replies. Yah, it very much makes sense now. I don't know why I couldn't make that leap of logic before.

Thanks again.
posted by mazniak at 8:28 PM on October 25

So could I assume that if the resistors were in series the sign would be +?
posted by weapons-grade pandemonium at 9:20 PM on October 25

Yes, weapons-grade-pandemonium.
posted by sonic meat machine at 9:59 PM on October 25 [1 favorite]

You could write the equation using the expanded form as GuyZero shows but the form in the book shows not only the mathematical relationship but also the geometric relationship. It more clearly represents the physical circuit and the derivation of the formula. Any set of parallel or set of series resistors can be replaced by a single equivalent resistor. An expanded and simplified form might look quite mysterious because it obscures these relationships.
posted by JackFlash at 12:33 AM on October 26

Also the formula for parallel resistance is awkward so the shorthand they use is a lot more readable in addition to representing the semantics of it as opposed to just the raw numbers. You'd have 3 or 4 levels of nested fractions in this example which would be fairly hard to parse.
posted by GuyZero at 9:16 AM on October 26