In a parallel circuit with a 4 ohm and a 2 ohm resistor and a 12 volt source, what is the potential difference across the 4 ohm resistor?

12volts

Explanation:

The potential difference between 4ohm resistor is 12volts because equal voltage is dropped in both resistor.

The picture clearly shows that the 4Ω resistor is connected directly to both terminals of the battery. If you connect a voltmeter to the ends of the resistor, the voltmeter is connected directly to the battery terminals. So the potential difference across the 4Ω resistor IS the potential difference across the battery . . . 12 volts.

As long as the battery is fresh enough to supply all the current that both resistors want, the 4Ω resistor doesn't even know that the 2Ω resistor is there. (And the feeling is mutual.)

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