Simplifying Electrical Mathematics in Certain Scenario

[The W]

When I was in school for Biomedical Engineering, while playing with numbers I noticed a pattern while calculating an equation, so I tested it. This is for relatively simple equations but maybe there is a way to incorporate it at a higher level. I would imagine while crunching numbers there may be some benefit. IE a computer calculating these parameters quicker. I can't remember the exact equation it held true for but it looks like it works on multiple equations now whilst using a calculator. This may prove useful in understanding electricity or perhaps even laying out a circuit, but what do I know, I'm just a dumb grunt.

If you are calculating inductance and L1 = 18 and L2 = 36, then the total inductance in parallel LP= 12...which is 1/3 of L2 or 2/3 of L1

This works for Capacitance for calculating the in-series value as well. Basically, if one value is half of the second value, then the value you are seeking is 2/3 of the initial value or 1/3 of the second. This can be thrown around in different ways and proves true in the cases I've tested. Not sure if some one else has discovered it but I just enjoy playing with patterns. Enjoy!

 

[berkeman]

Welcome to the PF.

How about you post the math for such combinations, and comment on why the patterns you are seeing are supported by the math?

There is a LaTeX tutorial under INFO at the top of the page, click on Help/How-To. It's best if you post using math symbols to make it easier for others to understand what you are saying. Thanks.

 

[Baluncore]

Many students notice the particular pattern, 1/6 + 1/3 = 1/2. Unfortunately, that pattern occurs more often in examples and exams than it does in the real world. That is because the invented problems are arranged to have simple integer answers.
It is very rare that two components in a real circuit will have values related by a factor of two. Why?

Firstly, power dissipation or breakdown voltage means that when two similar components are used in parallel or series, they will have identical values.

Secondly, most components are available in logarithmic steps. The common E12 series has 12 values in each decade. Each value increases by 10^(1/12) from the last = ratiometric steps of 1.2115; The closest values to a factor of two will be on either side of two, at 1.7783 or 2.1544; So to make two components having a ratio of two you will need to start with three identical components.

The same sort of problem occurs in western music, but then each 12 note octave steps by a factor of two. Each note is therefore a ratiometric step of 2^(1/12) = 1.059463; To generate a note with 10 times the frequency of another, the closest you can get is 10.0794;