Can someone tell me how the contents of a furnace affect a comparator? I want to create some automation in vanilla Minecraft, but don't know how the mechanics work.
This page has a paragraph specific to the power output through a comparator on a furnace.
It's pretty confusing, though.
Basically, for the full 15 signal you need something in all 3 slots of the furnace. If you're feeding in smeltables and fuel (assuming they are in the right places, and full), then anything above 10 would mean that there is something that has completed smelting.
That is probably over-simplified, but I hope that helps.
To further attempt to answer your question; The contents are summed and the resulting value of all contents are output through the comparator.