New Parallel Resistor Calculation Method

[paulfr]

TL;DR

The N + 1 Rule for Parallel Resistors

In teaching HS Physics part of which is Electric Circuits,
I have discovered a rule / technique for parallel resistors that I never encountered
in all my 30+ years in electronics engineering, nor in any textbook on Circuits.
It is what I call " The N + 1 Rule "

We all know the Reciprocal Rule
1 / RT = 1/R1 + 1/R2 + 1/R3 ... + 1/Rn

AND
we know that for 2 resistors, this becomes the Product over the Sum of the 2 R's

BUT
The N+1 Rule is this
1/ Find N = the ratio of the two R's
2/ Add 1 to it to get N + 1
3/ Divide the largest R by N+1

E.g.
4 and 20 ohms
N = 20/4 = 5
N+1 = 6
RT = Rtotal = 20/6 or 10/3
Check
Product = 80
Sum= 24
RT = 80/24 = 10/3

It is quite useful when the numbers are large and thus the Product is very large.
No need to remember it and then do long division.
e.g.
300 and 50 becomes much easier and thus faster with N+1 than with Product-Sum.
300/50 = 6 ==> Rtotal = 300/7
Check with Product Sum Rule
300 (50) / 300 + 50 = 15000/350 = 300/7

It works even when N is not an integer.
e.g.
500 and 300 ohms
500/300 + 1 = 5/3 + 1 = 8/3
Rtotal = 500 / (8/3) = 1500/8
Check with Product Sum Rule
500(300) / (500 + 300) = 150000 / 800 = 1500/8

Have any of you ever seen this ?

Just curious and wondering why it is not in all the textbooks on Circuits.

Comments solicited

 

[marcusl]

You have simply rearranged the usual formula by dividing numerator and denominator by one of the resistance values.
$$R=\frac{R_1R_2}{R_1+R_2}=\frac{R_1}{\frac{R_1}{R_2}+1}=\frac{R_1}{N+1}$$It doesn't matter which resistance you choose to divide through by (it could be the smaller).
Sorry, but there's nothing special going on here.

 

[davenn]

Summary: The N + 1 Rule for Parallel Resistors

Just curious and wondering why it is not in all the textbooks on Circuits.

because it's a really complex way to do it