When you add an armature, it comes with the first bone, in a vertical position, with the end selected (it’s highlighted yellow). You can grab (type g and move the mouse) the end of the bone and move it around so it is no longer vertical, if you like.
If you don’t move it, and add another bone, the new bone will be exactly the same size, in exactly the same place. It will look as if nothing has happened.
I suspect that what you want is a chain of bones, with the second bone attached to the end of the first one. If so, then instead of adding a new bone, extrude the new bone (type e with the end of the old bone selected, then move your mouse to extrude the new bone.)