Two identical bulbs are joined one after the other in a single loop with a battery

Why

Vikram's picture is a reasonable one — the battery clearly gives something out, so it seems the far bulb should only get the leftovers. But current is not fuel being spent; it is charge flowing round a closed loop, and in a single loop the same flow passes through every single part of it. What the bulbs use up is energy, not current, and they take their share equally. Picture water in a closed ring of pipe with two identical taps in it — the same water passes both, and none of it vanishes at the first. Test: swap the two bulbs over. If position mattered, the bright one would move; it does not. Neha is right: in one loop the current is the same everywhere.