## Friday, April 29, 2016

### Examples of vector utility

If you buy a resistor its usefulness in a given electronic circuit depends upon, at least, its electrical resistance, R, and the power it can withstand, P.  It has a vector utility of at least U = (R, P).  The utility might also depend upon the dollar cost of the component and its physical size as well.

If you buy a capacitor its usefulness depends upon, at least, its capacitance, C, and the maximum voltage it can tolerate, V.  Its vector utility is then, at least, U = (C, V). No single scalar utility can be assigned to the capacitor unless you can specify its application.  If the capacitor is to store charge, say as a memory cell, then perhaps a suitable scalar utility would be U = Q = CV.  On the other hand, if the capacitor is intended to store energy, say in a capacitor bank, then perhaps a suitable scalar utility would be U = E = .5 C VV.  If you wish to store charge while using a minimum energy then perhaps U = Q/E = 2/V.  A suitable scalar utility depends upon the context at the moment. A general utility needs to be a vector. (See chapter 2 of my book, Twelve Papers, www.robert-w-jones.com , book.)