I don't understand why. To be fair I don't understand anything at all. I treat current like a river and voltage like a difference in height between different parts of the river flow. As I understand inductor saves energy when you make changes in current flow, and releases it in form of voltage when the flow is steady (no matter how large it is). Am I dumb?In Figure 1.52A the left-hand side of inductor L is alternately switched between a dc input voltage Vin and ground, at some rapid rate, spending equal times connected to each (a “50% duty cycle”). But the defining equation V =L dI/dt requires that the average voltage across an inductor must be zero, otherwise the magnitude of its average current is rising without limit. (This is sometimes called the volt-second balance rule.) From this it follows that the average output voltage is half the input voltage (make sure you understand why)