Finding Current in a Parallel Circuit with Multiple Resistors

[Ry122]

Homework Statement

Im aware that you can find the current passing through each resistor in a parallel circuit by using the equation I=v/r but for homework i was asked how to find the current by using the ratios between each resistor.
eg.
---5ohms---- Resistor 1
- 20ohm - Resistor 2
- 10ohms - Resistor 3
----| - |-----
I=20AMPS
If only resistor 1 and 2 exists i can do it by dividing 5 by 5+20 and dividing
20 by 2+20. Inverting the results so 5/25 is for resistor 2 and vice versa then multiplying the results by 20amps. This gives the amps passing through each resistor.
I've no idea how to do it if there is 3 or more resistors.

Homework Equations

The Attempt at a Solution

 

[denverdoc]

On the right track--we know that current is inversely proportional to resistance, so let's set up the eqn with a little i which is the current flowing thru the 20 ohm resistor: In fact, this makes use of the V=iR eqn at least implicitly, assuming 20 amps total passes thru the branch.

i+20/10*i+20/5*i=20A=7i. i=20/7, etc.

Now if 20 amps passes thru say the small resistor, and total current is unknown,

then (5/10)*20 will pass thru the 10 ohm and (5/20)*20 thru the 20 ohm.