If you're an Apple user, and one that uses their power adapter like it's supposed to be used, you will eventually see something like this happen. If you're lucky, the adapter will still charge. If you're not so lucky, it won't charge at all.
In this situation, if you're lucky enough for the break to occur close to the brick, you can cut and strip without losing too much length. Otherwise, you'll need to spend $15 on something like this: http://www.ebay.com/itm/APPLE-A1184-A1330-A1172-A1222-A1290-60W-85W-Magsafe-AC-Adapter-DC-Cord-Repair-/220967191974?pt=Laptop_Adapters_Chargers&hash=item3372abc5a6
Cut, and strip. You'll find one insulation white, and braiding. This braiding is actually the "black" wire soldered inside. You'll need some heat shrink tubing to give the "black" wire insulation.
|Stripped and braiding wrapped into new "black" wire.|