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## Summary:

- 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

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