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While watching a video lecture, I became uncomfortable with the results, (around 35 mins). The professor draws an electric circuit with a 1V batter, and two resistors (1 and 9 ohms). He then calculates the voltage across the 9 ohm resistor and the voltage across the battery and 1 ohm resistor so that they are the same. So far so good. Then, he "replaces" the battery with a solenoid.

This is what I don't understand: How can he just replace a battery with a solenoid? He then calculates the voltage across the solenoid and 1 ohm resistor and it is different from the voltage across the 9 ohm resistor. He then adds the two different voltages to obtain the voltage supplied by the battery. He claims that this is because of non-conservative fields. I think he is right I just don't fully understand what the point of hypothetically switching out a battery for a solenoid is.

What exactly is the point? We can't do this in real life without the voltage disappearing, so this seems almost like a thought experiment.

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He does not replace the battery by a solenoid. The whole circut is the solenoid. The voltage induced in the circuit is 1V, therefore, going around the circuit leads to a voltage increase by 1V.

We can't do this in real life without the voltage disappearing, so this seems almost like a thought experiment.

Yes we can. At about minute 46 he actually shows the experiment.

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    $\begingroup$ Ohhh! He doesn't repace the battery with a solenoid he replaces the battery with an induced EMF due to changing magnetic flux! I kinda missed that. I think he could have said it better: he began by saying at 38:52, "I am going to replace the battery by a solenoid." I thought he meant he was placing a solenoid in the circuit where the battery was so that the magnetic field came out of the board. haha. $\endgroup$
    – Dale
    May 19, 2013 at 18:57

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