Flux & Physics: Explaining the Constancy of Flux

[harsh22902]

This is an excerpt from a high school physics textbook. I don't understand the possible reason behind this statement. If we change something in the circuit say for example add a resistor , the current and hence the flux should change. Then why/how is this statement true?

 

[BvU]

Correct, but not instantaneously: it takes time. https://www.electronics-tutorials.ws/inductor/lr-circuits.html is $L/R$