Equivalent resistance problem

[dcnetsfan77]

Hey guys,

I dont know why I am stumped....I dont understand how for parallel resistors (3 or more all the same resistance) can equal Req= R/n (n being number of resistors)

The reason I am confused is because if you take an example with 3 resistors in parallel, all with resistance 2 ohms you get : 2x2x2/(2+2+2) = 8/6

Then if using Req=R/n: 2/3 ???

I must be doing something wrong here, this is coming indirectly from a TPR problem, passage 30 in physics number 5 in the science workbook

THANKS!

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[NextStepTutor_1]

The equation for parallel resistors is as follows:

1/Req = 1/R1 + 1/R2 + 1/R3 + ...

For two resistors, the algebra works out to be :

Req = R1*R2/(R1+R2), however, that doesn't mean you can just add R3 in there and make that correct. Instead, you have to go back to the original equation.

So if all the resistors have the same value R, we get :

1/Req = 1/R + 1/R + 1/R

1/Req = 3/R

So, Req = R/3.

We can repeat this with as many resistors as needed, but the algebra still holds so that Req = R/n

 

[patrickmbyrne]

A useful thing to note is that for two resistors in parallel the resistance will be half. 2||2 = 1.

 

[DrknoSDN]

I must be doing something wrong here, this is coming indirectly from a TPR problem, passage 30 in physics number 5 in the science workbook

TPR Physics 2010 page 266 paragraph 3:
"The 'product over sum' formula for parallel resistors only works for two resistors. If you have three or more resistors in parallel, do them two at a time. Here's an example:"

It shows how to use the Product/Sum trick for 3 non equivalent resistors on that page.

 

[dcnetsfan77]

Thank you very much! this makes a lot of sense now..obviously im burning out because I knew I was missing some simple fact