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Unread 08-01-2003, 18:36
DanL DanL is offline
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Robotics and Calculus?! Oh nos!

A funny thing happened to me while I was doing my calc homework. It happened that I had to do the following problem in my textbook:

Quote:
The formula for the power output P of a battery is P = VI - RI^2 where V is the electromotice force in volts, R is the resistance, and I is the current. Find the current (measured in amperes) that corresponds to a maximum value of P in a batter for which V=12 volts and R = .5 ohm. Assume that a 15-ampere fuse bounds the output in the interval 0 <= I <= 15... <more parts that aren't relative to question>
Anyways, the point is to use the derivative to find the critical point, and then plug that in to the origional equation to find the maximum value. What it comes down to is the maximum power of 72 (joules?) is achieved at 12 amperes. I'm guessing what that means is peak efficiency is at 12amps, 12 volts, and .5 ohms.

What I want to know is can you apply this to robotics somehow? Can we, for example, find the voltage and the amperage for a certain component and adjust the resistance to get it closest to peak efficiency for the battery? Or is there more to this concept than a mere problem in a textbook implies?
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