The question then asks for the potential difference between X and Y, which is cl

Question

The question then asks for the potential difference between X and Y, which is claimed to be 3.6 volts.

Why would there be a potential difference in this case? If I connect a lightbulb on X, and another on Y, it seems very obvious that the brightness would be the same.

Or is the standard direction of current important? So the current "encounters" the 60 ohm "first" when flowing to X, and the 30 ohm "second" when flowing to Y? That seems a little crackpot to me. So if we change the resistor to the left of X to 100 ohms, and the resistor to the right of Y to be 0 ohms, the differing definitions of current flow would actually cause a difference in measurement of potential?!?!

The correct answer is worded:

Explanation / Answer

Try the following two thought experiments.

Eliminate the branch of the circuit containing Y. You now have three resistors: the internal resistance of the battery (5?), and the two given resistors. Whatever current you determine to flow through the circuit, it must be the same through all three of those resistors. Because of that, the voltage drop across the 60? resistor has to be exactly twice the resistance drop across the 30? resistor.

Eliminate the branch of the circuit containing X. All of the above still holds, except that the ordering of the resistors is different.

Now reassemble the circuit. Because the two branches have the same total resistance (30?+60?=60?+30?=90?), they have the same current running through them. If you change the values of the resistors, then the current might not be split equally between the two branches. But the voltage drop across the two branches will always be equal, regardless of what the total current is or how it is split between the two branches. And the voltage drop within a given branch will always be divided between that branch's resistors proportionally to their resistance values.

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