Also, the best way to explain it, is to tell someone to leave their DS/DS Lite on, with Wi-fi activated, all the time they're playing. Best place would be to test is on Animal Crossing, since that's achievable. You're going to have it die, quickly. Especially if it's on the Lite, with the improved screen brightness. No-one considers how much the Wi-Fi eats at your battery; but I know it for a fact: There's a reason I consistently plug in my DS to charge if I go to play a game over Wi-Fi on that. The Wi-Fi drains the battery quicker than anything.
63084
I can testify to this, the same thing happens to laptops. I was once watching a movie on my laptop at about 30% battery power. I accidentally hit the shortcut key that turned the wifi on, and in less than a minute the laptop shut off due to low power.

Though why Nintendo didn't use a smartphone-level battery for the 3DS is beyond me; they really didn't think that one through. (In fact, Blade, I'd recommend doing some modifications to your 3DS to swap out the DSi battery with something from a modern smartphone--I imagine it would be fairly doable, and would dramatically increase the battery life.

)