Let's get started with the Armor Class of the example character now!
Armor Class
Our example character has a wealth of Armor Class improvements:
+7 armor bonus (+2 chainmail)
+2 shield bonus (heavy shield)
+1 deflection bonus (ring of protection +1)
+2 natural armor (barkskin spell)
+2 Dexterity bonus (the character's Dexterity is 17, thanks to the cat's grace spell, but chainmail allows only a +2 Dexterity bonus to Armor Class, says Table 7-6 in the Player's Handbook).
+4 armor bonus (mage armor spell)
+4 shield bonus (shield spell)
+2 deflection bonus (shield of faith spell)
That's a lot of bonuses, but all the bonuses with the same names overlap, so we're left with the following:
+7 armor bonus (+2chainmail)
+2 natural armor (barkskin spell)
+2 bonus from Dexterity (from the cat's grace spell, as limited by the chainmail)
+4 shield bonus (shield spell)
+2 deflection bonus (shield of faith spell)
That's a total bonus of +17 to Armor Class, giving our example human (who has a base Armor Class of 10 with no size adjustment) an Armor Class of 27.
Please note a couple of things here:
Multiple Enhancement Bonuses: The character is effectively getting two enhancement bonuses to Armor Class (from the +2 chainmail and the barkskin spell), and that works in this case because those two bonuses are being applied to two different elements of the character's Armor Class.
WhereEnhancement Bonuses Apply: In general, an enhancement bonus goes with a specific item a character uses, or with one of the user's abilities or other statistics. The example character's touch Armor Class is only 14, because a touch attack bypasses the character's armor bonus (including the +2 from the magic armor), natural armor bonus (including the +2 from the barkskin spell), and shield bonus. Those enhancement bonuses don't float around the character, warding off harm; they improve a specific aspect of the character's defenses.
Overlapping Bonuses are Still in Place: This can become significant when dealing with Armor Class. For example, our human has an Armor Class of 24 against an incorporeal touch attack, as follows:
Base 10
+2 Dexterity: The chainmail's Dexterity cap still applies, even though the chainmail itself can't block the attack.
+4 shield bonus: The shield spell works against the attack because it is a force effect.
+4 armor bonus: The mage armor spell works against the attack because it is a force effect. (But, neither the chainmail's +2 enhancement bonus nor the barkskin's +2 enhancement bonus improve the mage armor's armor bonus.)
+2 deflection bonus from shield of faith spell.