Two questions on voltage regulators

If have a circuit that needs 5V, and I have a battery that generates 9V, I
can wire a couple of resisters into a voltage divider, and have a 5V
supply. But the big "but" is that you're throwing away nearly half the
energy in the battery, dissipated as heat in the resisters.

Do voltage regulators do the same, internally? Do they limit the current
supplied externally by throwing away the excess? Or are they more
friendly to battery life?

Second - batteries come with two ratings - Volts and Amp-Hours. (Or
milliamp-hours in the usual sizes.)

Strictly by dimensional analysis, the energy stored in the battery is the
product of the two - Watts = Volts * Amps, so Volts * Amp-Hours =
Watt-Hours.

Suppose you have a 12V battery with a 60 mAH rating. If you plug it into
a DC circuit with 600 Ohms of resistance, you'll get a 20 mA draw. And
you can expect about 3 hours of battery life.

But suppose I have a circuit that has wants 3V and a 20mA draw, and I use
a voltage regulator to drop the voltage. It's still a 20mA draw, so
should I expect 3 hours of battery life? Or could I expect 12?

--
..Sig?
.

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