Korkhoff's Loop Rule: Proving Current Ratios

[okgo]

http://www.screencast.com/users/trinhn812/folders/Jing/media/3bedaa97-7020-4c5b-85d8-213de24b30a5

For the above problem. A helpful yahoo user told me that I can prove the answer for the above question by solving the problem. He said:

Total current is 9/6.2 = 1.45 amps.
that all flows thru the 5Ω, and 3/5 of that goes thru the 2Ω (0.87) and 2/5 thru the 3Ω (0.58).

So I understand how to prove that his ratio is correct with Korkhoff's loop rule.

But I was wondering how he got the ratio 3/5 for the current of the 2Ω and 2/5 for the 3Ω resistors without using the loop rule. Is it just intuitive?

 

[Mindscrape]

Yes, it is just intuitive, but it may take awhile to develop circuit intuition before you can get there yourself. Current takes the path of least resistance (or impedance if you get really far into circuits). Don't even use numbers to solve a problem that doesn't need them. :)