A reader was confused by the units in the power problem of 1W.2
A reader writes “On Page 47, we’re asked to calculate the smallest 1/4W resistor to be put across a 5V supply. The solution gives P=V^2/R which is correct, but the formula after says R=25^2/0.25 which gives an answer of 2k5 ohms. Not the actual answer which should be R=5^2/0.25=100 ohms.”
I responded:
I see why you are confused but the “V2” in the formula in the solution are the units for the value “25.” The “V” in the units is squared but the “25” has already been squared (5 V* 5V = 25 V*V=25 V2).
Since this example occurs early in the book, we are trying to show how electrical units relate to each other and we want to encourage students to include the units with values in their calculations.
In teaching this stuff we find students often do not carry units though their work and they miss obvious mistakes as a result. (For example, had this calculation used “5V,” the result would have been inverse amps, not Ohms, but if we had written just “5” without the units the mistake would have been less obvious).
Checking units is an easy way to catch errors, particularly when one is still unfamiliar with a subject (although even with years of experience I still include units in my calculations as a check against a mistake). It is too bad we don’t have a symbol for volts-squared, since that would have avoided the confusion.