/diy/ - Do It Yourself

>In Figure 1.52A the left-hand side of inductor L is alternately switched between a dc input voltage V in 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).

I don't understand why it's half.
Also, I'm a Comp E student and have only taken two EE classes. Basically the extent of my knowledge is passive circuit analysis/filters, Laplace transforms, and some op-amps. I wanted to read the Art of Electronics to get a more practical perspective, because even though I do fine in the classes, sometimes I only feel like I know how to solve math problems. Should I continue with AoE, or pick something else up?