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question about linear regulators....

A regulator will provide a constant voltage regardless of the supply voltage (as long as the supply voltage is sufficient to cover the load voltage + regulator drop out). So, if supply voltage can vary (e.g. due to mains voltage fluctuations; ripple in a rectified AC system; batteries at variable states of charge; etc.) but a constant output voltage is required, then a regulator is desirable.
 
Voltage dividers have no regulation capabilities; if the input voltage changes, the output changes. If the load changes, the output voltage changes. They are also very wasteful of power.

Like Mark said, linear regulators provided a constant output voltage regardless of output current and input voltage within limits - the output voltage must be a certain amount (typically ~1.3 volts) lower than the input. They are wasteful, though, since they burn off the excess as heat - power wasted is (Vin-Vout)*Iout, which is severely limiting in some cases.

Linear regulators are very electrically quiet and simple vs. switching regulators, but switching regulation is better all around; any input voltage can be converted to any output voltage, and efficiencies can top 90% since they depend only on the circuit construction and component quality rather than the input and output loads and currents, although high-voltage-drop buck regulators tend to be not as efficient.

Switchers can also be a lot smaller due to their higher efficiency - if a 12V -> 5V converter needs to supply 15A (think computers), a linear regulator would be burning (12-5)*15 = 105 W of energy as heat. That's like having an overclocked P4 sucking up extra power. A switching regulator at 90% efficiency would only lose (5*15)(1/0.9 - 1) = 8 1/3 W of wasted energy as heat. The advantages are obvious!
 
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