Understanding Power Sources: Solving a Circuit Question with V=IR Method

[shibme]

Homework Statement

- see image

Homework Equations

I am having trouble figuring this out mathematically...

I have no idea why but I can't figure it out using V=IR that the circuit on the left has 1/3 the current of the circuit on the right...

can anyone please give a mathematical explanation?

The Attempt at a Solution

Left : 3Vb = I1 * RL
Right : Vb = I2 * RL

then if Vb = 2 and RL = 1, wouldn't that make I1 > I2, by 3 times..

anyone suggestions?

 

[interested_learner]

Your solution is correct.

 

[shibme]

hmm... this question is actually from the book and the answer is in words... it states that the circuit on the right (I2) should be 3x the current on the left (I1), but according to my calculations that is not the case... I can't figure this out mathematically...