2025.05.25 06:29
graphical determination of the equivalent resistance of resistors connected in parallel
I came up with a way to graphically determine the equivalent resistance of resistors connected in parallel. See the drawing:
Let's assume I connected two resistors in parallel with resistances of 6 Ω and 4 Ω, and I want to calculate the equivalent resistance. On graph paper, I draw two vertical lines (AC and BD) with lengths 6 and 4. I connect points C to B and A to D with diagonal lines. I mark the intersection of segments CB and AD as point E. I measure the height of this point (in my drawing it's the length of segment FE). As you can see, in my drawing the result came out to be 2.4 Ω, which is 12/5 Ω, so it's correct.
I can prove (using Thales's theorem) that this really works, but I have no intuition as to why.
In the same way, I can determine the time needed to fill a bathtub using two taps, where one fills the tub in 6 minutes and the other in 4 minutes, because it's the same mathematical relationship.
comments:
back to homepage
RSS