Even though both the voltage v and current i are both functions of time, they are in phase with each other so their ratio is a constant. Being in phase means they both reach their maxima at the same time, both pass through zero at the same time, and both reach their minima at the same time.
As the voltage v increases, the current i increases proportionally so that the ratio of v/i remains a constant. This constant is the resistance R. While we can write this resistance as
it might be mistaken to imply that the resistance varies with time; the resistance R is a constant. We can also write the resistance R as
where the voltage or potential difference is given by
and the current is given by
Vmax , Vo , Imax , and Io are just ordinary numbers or constants so they are written as capitals.
(c) Doug Davis, 2002; all rights reserved
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