Why is a bulb lit as soon as a torch is switched on?

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The vibrations they cause as they drift under the influence of the voltage creates heat which quickly heats the filament to white hot.
 
The electrons might move relatively slowly, but the wire is already full of them, so once the first ones start to move, a pressure wave moves through the wire (at the speed of light) causing all of them to start moving very soon.

For the same reason, water starts pouring out of your faucet almost instantly after you turn it on.
 
Addendum: Imagine a street full of crowded people milling around. Someone yells Free Beer! from one end of the street creating a desire to move in one direction. They're crowded so they don't move quickly but their bustling and bumping into each other will cause quite a loud ruckus quite quickly. The light from the filament is the electrons yelling for free beer as they bump along. ;)
 
You could also think of it in terms of marbles in a tube. Where the marbles represent electrons and the tube represents the wire. If you push a marble in one end of the tube, another marble will come out the other end almost instantaneously. Even though the marbles are actually moving very slowly, the force moves from one to the other with great speed. It's the same in a wire. Even though the electrons are only moving at 0.03miles/hr, the wave fronts are moving much, much faster.
 
jambaugh said:
Addendum: Imagine a street full of crowded people milling around. Someone yells Free Beer! from one end of the street creating a desire to move in one direction. They're crowded so they don't move quickly but their bustling and bumping into each other will cause quite a loud ruckus quite quickly. The light from the filament is the electrons yelling for free beer as they bump along. ;)

Now that clears it up!