What in the world are ohms?!

[Bobbsy]

 

Two 8 ohm speakers do indeed (roughly) present a 4 ohm load. But to get down to 2 ohms takes two more, not just one more. 3 8 ohm speakers in parallel come out at nearer 3 ohms - a fairly trivial difference, but 'every additional speaker roughly halves the impedance' isn't really quite true.

 

That's why a said "roughly". I wondered if somebody would pick up on it but my guess was that anyone who had to ask what an ohm was wouldn't be ready for the necessary maths and, in any case, was pretty unlikely to be renting any amps that could safely and reliably go below 4 ohms. Basically, I was trying to scare him off!

[dbuckley]

1/Rtotal = 1/R1 + 1/R2 + 1/R3 ... + 1/Rn

 

There is a shortcut though... for two resistors in parallel: (r1 x r2) / (r1 + r2). Simple enough to do in the head, unlike reciprocals.

 

For three resistors do it in two chunks.

 

So for two 8 ohm speakers, its eight squared over eight doubled, so 64 / 16 = 4.

 

Add a third speaker of eight ohms, given we already know that two of them are four ohms, its (8 x 4) / (8 + 4) so 32/12 which is a bit less that 36/12 which would be three ohms.

[paulears]

1 suspect the standard of GCSE maths has been over estimated. When I was teaching, I got given the group of performing arts people because the Government decided average numeracy levels were grim. As the only teacher with A Level maths, it fell to me. No calculators. Means, modes and medians came up in the list - Boss said they MUST pass. Lots of educational looks and face twitches, stage eye looks at 'new build' plans on the wall. No calculators. Try to think with a crafty tilt. Seat prices! I gave them a list of ten seat prices for shows at a venue and asked them to find the mean. I thought this sorted the no calculator rule nicely - but still blank expressions. "So, you've added up the ten prices then?" heads nodded. One girl opened her mouth "Ok smartarse, but how are we supposed to divide it by ten without calculators?" I was gobsmacked - so suggested almost incredulously, "er, move the decimal point to the left?" the girl did it, then produced her phone, and used the calculator to check her result and her mouth dropped open. She then had a quizical expression. "Does that mean moving it the other way times it? I nodded - she checked and smiled. "That's pretty cool" she said. Ten minutes later, they all had correct answers. Annoying though this was, it was not really their fault. Nobody had ever told them. We checked and found they'd all gone to the same middle school (Norfolk loved those). Nobody ever spotted this glaring hole, because calculators were allowed.

 

My guess is that many of our members may not understand (r1 x r2) / (r1 + r2).