Do you get better gas mileage with the radio off??
I've heard that it does, but the amount of fuel saved is so small, I'm not even sure if it could be measured. The radio takes power and the power comes from the alternator. Any more drag on the alternator is going to result in less fuel economy and power.
I have never turned off the radio to save gas myself. I'm not going to give up my tunes in attempt to get maybe .24MPG better. If even that much.
I always thought the alternator puts out the same amount of power, but the voltage regulator limits the amount to the battery.
It should not take any more gas to send a little more power from the regulator to the battery, because the radio is on.
The voltage regulator is to regulate the voltage to recharge the battery. The alt does make more, but power isn't free. When you turn on the lights or use any electrical device on your car, it takes more power to turn the alt.
If you knew how to get power from nothing, well, you would be wasting your time on this forum.
If the regulator limits the power coming from the alternator, and the alternator puts out more power than the minimum need to operate everything on the car, it would not take any additional gas to keep it running the same amount. If there was a problem due to additional accessories, higher output alternators are also available.
When you turn on the lights, it drains more from the battery, but the regulator just increases a corresponding amount of power coming from the alternator, without making the alternator do any additional work. That isn't power from nothing, it still burns the same gas.