I am trying to get some things straight about the average voltage across an inductor an am stumbling a bit (mostly due to my inability to solve some differential equations).

I know that in steady state analysis, the average voltage across an inductor will always be 0 because you're dealing with sinusoids.

Is this always the case in an inductor?

 

Yes, in steady state the average voltage across inductor is always 0V
http://forum.allaboutcircuits.com/showthread.php?p=283016#post283016

 

Right, but I mean beyond steady state is it always true? For example, a circuit with an AC source in series with a battery and an inductor....would the average voltage not be 0 in this case? What does that imply in terms of the inductor's behavior? In most diode rectifier circuits I've looked at it's also true, but I'm not sure if it is true across the board.