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

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The discussion centers on a circuit analysis problem using the V=IR method, where the user struggles to understand why the current in one circuit is one-third that of another. The user sets up equations based on the circuits but concludes that their calculations suggest the opposite relationship. Despite the textbook stating that the current in the right circuit (I2) should be three times that of the left (I1), the user finds their results contradictory. The confusion arises from the application of the voltage and resistance values in the equations. Clarification on the mathematical approach is sought to resolve the discrepancy in understanding the current relationship between the two circuits.
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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?
 

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Your solution is correct.
 
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...
 
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