Re: What do headlights run off of when your car is running?

When a car's engine is off, lights (radio, and other accessories) do 
operate only from the battery.  When the engine starts, the alternator 
supplies power to recharge the battery and operate the electrical 
accessories.  

You can think of a car battery as a large bucket of water.  The bottom of 
the bucket has holes in it that let some of the water out.  Lights, radio, 
and other accessories amount to such holes.  When the bucket is full, this 
is equivalent to the battery being fully charged.  Water flows quickly 
from any hole.  However, in time, the bucket empties and the flow slows 
down.  This is equivalent to the battery becoming discharged.

The alternator charges the battery--fills the bucket.  An alternator is a 
wild frequency alternating current (AC) generator.  It is called wild 
frequency because the frequency varies, depending on the speed of the 
engine.  It is called alternating current because the current flows 
alternately in one direction, then the other. 

The charging control rectifies this alternating current to make it a 
pulsating direct current.  It also limits the alternator voltage to a 
level that will charge the battery, but not overcharge and overheat it.  

You may think of this alternator and charging control as a water pump that 
is used to fill the bucket.  Being a rectified alternating current, the 
water that refills the bucket has a pulsing character to its flow.

Now we have an analog to your question.  When the engine is running, and 
the lights are on, we have a bucket that is being kept full of water, but 
is still leaking at the same time.  On average, the pump (alternator) 
supplies the water (electric) current flow.  Because of the pulsing nature 
of the pump's (alternator's) output, the bucket (battery) still supplies 
current during bottom of these pulses.  

The following URL's can be clicked with your mouse to go to sites that 
will tell you more about car batteries, alternators, and their controls.
 http://www.hotrodssuperstore.com/super-store/intoel.html
 http://www.eatel.net/~amptech/elecdisc/charging.htm