>>473
In your example, anything can follow the former sentence as long as it makes sense while it is more natural if the のだ version is followed by something like だからおなかいっぱい (so my tummy is full now). So if you reply, "林檎を食べました" when you're asked why you skip lunch, it sounds a little awkward, but 林檎を食べたんだ is natural.
Grammatically んだ is a spoken form of のだ, which places an emphasis on reason, determination, or meaning. But in reality, most of the time んだ just smooths the path to the next sentence or makes the meaning clear by restricting possible connotations/implications. I think it emphasizes a sentence only when the speaker's voice and expression is strict/harsh/whatever, in which case you're pretty sure about that anyway.