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List two advantage of a variable regulated dc power supply over cells batteries?

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  1. 1. Assuming the power supply is of a decent quality, once you get a fairly consistent power output, for pretty much as long as you need (as it's usually connected to AC).  Batteries run out eventually, and as they do, most have a downward voltage curve, where the voltage drops off gradually as the power runs out.    So with those (eg. carbon, and alkaline), the battery might not stay within the required power spec during it's lifespan.   It might still be able to run other devices, but some circuits may not behave properly unless the right current and voltage are supplied.   With other battery types, the voltage curve stays pretty steady right up until it dies, and then the voltage curve kind of drops off a cliff (you see this with NiCads).   Either way, you're stuck with a dead device until you get some fresh batteries.

    2. Variable power supplies let you dial in exactly the voltage you need.   Well, not exactly, as we live in the real world, and there are always variances, but you can dial it in pretty close.  With cells, unless you want to mix and match different types of cells, you're going to have to live with voltages that are multiples of whatever voltage output one cell is.   For example, the most common Alkaline batteries have a power output of 1.5V.   You can achieve higher voltages by stacking cells in series, which can give you voltages of 1.5V, 3.0V, 4.5V, or 6V.   If you need 5V for a circuit, you have to either hope that it will run properly at 4.5V, or that it's robust enough that it won't fry at 6V.  There are ways around it, by adding a solid state power regulator to knock down that 6V to 5V, or by juggling cell arrays in parallel in the hopes of making something closer to 5V.   It's a bit of a pain though.

    There might be others, and I can't be sure that's quite what you're looking for, as I'm answering from the point of view of a electronics hobbyist here.

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