Potential applied across two points with batteries

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SUMMARY

The discussion focuses on the principles of voltage addition in electrical circuits, specifically addressing the behavior of batteries in series versus parallel configurations. It is established that when batteries are connected in series, their voltages combine, while parallel configurations do not affect the total voltage in the same way. The participant clarifies that the change in potential is independent of the path taken in the circuit, confirming that calculations can be performed using different paths without altering the outcome.

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1MileCrash
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Homework Statement



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The Attempt at a Solution



The first two were pretty simple, but I'm having trouble grasping why my guess for #3 was actually correct. Why are we ignoring the parallel battery/resistor combo up top and just adding the voltages of the two batteries in series?

As I understand it, batteries in series do add voltages, so I get that, I just don't understand why that other battery/resistor has no effect.
 

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the change in potential is not path dependent. So you can calculate the change using the upper path, or as you have done, using the (simpler) lower path.

Edit: you can also calculate the change in potential by using a path that goes through E3 then R1, it will still get you the same answer.
 

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