# Help Understanding Non-conservative Fields

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.