The effective value of a current which is composed of any number of sinusoidal currents of different frequencies can be expressed as:
Ieff = SQR(I1eff2 + I2eff2 + ... + INeff2)
source: Engineering Circuit Analysis (6th Edition), by William H. Hayt / AC Circuit Power Analysis - Page 369
This formula has caused me a lot of headaches because of the (illogical?) word: "different".... Lets consider two sinusoidal currents: I1=10sqr(2)cos(wt), I2=10sqr(2)cos(5t); So, I1eff=10, I2eff=10...
Now according to the way it is calculated:
Ieff = 10sqr(2), for all |w| != 5
Ieff = 20, for all |w| == 5
In other words:
Ieff(w=5+) = Ieff(w=5-) = 10sqr(2)
while, Ieff(w=5) = 20
The discontinuity in the function of Ieff is very obvious! The existance of this discontinuity is very questionable, especially in the current context.. Thats unnatural! You cannot prove two physical (even mathmatical) quantities to be equal! Since we cannot prove that two quantities are equal, it makes sense that an equation that works for different values of some variables, work also for equal ones....
In short, I think that the given equation is missing: Maybe, the details were skipped for simplicity, or maybe that author himself doesnt know what the fuck he's talking... If so, this might be an interesting area to investigate!
Update: (Jan 10, 2007) This problem has been resolved. Read more here.
PS: sqr(x) is square root of x
PS: The scientific validity of claims is NOT asserted