By Charles George Lamb
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Extra info for Alternating Currents -A Text-Book for Students of Engineering
But dO. this can be written o sum of two integrals by using the substitution on page 13, by considering the current as having the two components respectively in phase with and in quadrature with the pressure. as the that is We thus get W = EC ZTT -= ECW=^ , or r 27r 2 I Jo f (sin . 27r cos /I f ^cosX X sin - cos 20\ But the integrals of sin 20 and cos necessarily zero, and hence we have EC w W= -= 7T . ZTT With sine pressures is \/2 times the cos . COS X sin . sin X) . 20 20 over a complete period are EC = -TC COS X.
Owing Eddy current loss. In deriving the current from the cyclic curve the hysteresis loss was alone considered. In addition to this there is necessarily a loss due to the production of eddy currents in the iron core. The following experiment will show that such currents must to some extent be taken into account. Fig. 42. A choking coil was fed with alternating currents at different periodicities and different pressures, but the two quantities were so adjusted that the pressure was proportional to the periodicity and hence the maximum induction in the iron was always the same, the ohmic drop being in this case negligible.
Then #102 at =i eS) and hence any instant we evidently have e + e2 2 But the instantaneous power is given by e\ 02 )- W l the product w= j ^T. - el into the current, that is by e^ - e*). $2 and 3 denote the readings of the three voltmeters, that is the root of the mean denote the mean square pressures, and if power that is being delivered to the circuit, it will be readily seen , W that W = ^R ^ ~ ^ ~ ^ In many cases it is difficult to obtain a known non-inductive resistance for R. Instead of this we can use some ordinary incandescent lamps but in this case the value of will be unknown ; in order to find that value an ammeter can be placed in series R MEASUREMENT OF POWER 39 with them, and from the reading of this and the voltmeter we can find the value of R.
Alternating Currents -A Text-Book for Students of Engineering by Charles George Lamb