Page:Electricity (1912) Kapp.djvu/214

210 revolution the instantaneous value of the current. Thus the value of the A.C. corresponding to the vector position A is AB. The instantaneous value of the power at that moment is the product of the current AB into the e.m.f. over the lamp terminals at that moment. Now this e.m.f. is, by Ohm’s law, the product of current and resistance, so that the instantaneous power is proportional to the square of the length AB. If, then, we wish to ascertain What will be the average power during a complete cycle, we would have to draw the vector in all the positions given by the marked-out points on the circle, square all the lengths, add the squares up, and divide by the number of positions to which we have applied this arithmetical process. Taking the square root of this figure gives a length, and measuring this length with the ampere scale which we originally used in determining the length of the vector current, we get the effective current. To actually carry out such a calculation would be very laborious; fortunately we can avoid this mathematical drudgery by making use of the well-known Pythagorean axiom that the sum of the squares of the kathetes in a rectangular triangle is equal to the square of the