thatoneguy
- Joined Feb 19, 2009
- 6,359
Wouldn't you want to show the matrix abstraction of that, rather than stating the product/sum of products? That is the equation that I found a bit confusing when I just started (age 12). It wasn't explained 'why' it works until a college course. Prior to that, it was stated \(\frac{R1\cdot R2}{R1+R2}\) would only work for two resistors.Hi
I too use the inverse to illustrate parallel resistors. I'd like to see "s" adopted as a standard inverse r too.
The approach can be illustrated for three or more resistors:
I=(s1+s2+s3)V
=>R = (R1.R2.R3)/(R2.R3 + R3.R1 + R1.R2)
and for (n) in parallel the approach is
top line= product of all
bottom line = sum of the products of (n-1) terms, skipping one resistor in each term each time
You can see above that we skipped R1 in the first term, R2 in the second ...