EMF 



24 Messrs. E. B. Rosa and A. W. Smith on a Resonance 



To illustrate this point let us take a special case. Suppose 

 the resistance R is 500 ohms and the inductance of the shunt- 

 circuit, including both the resistance R and the movable coil 

 of the wattmeter, is 0'003 henry, %7rn being 800. Then 

 ^L = 2-4 and tan (^ = 0-0048, ^ = 16' 30", the angle of 

 lag of the shunt-current behind the electromotive force. 

 Suppose the true angle of the condenser-current, <£ 2 (fig. 4), is 

 89° 40' ahead of the electro- 

 motive force. Then the dif- 

 ference of phase of the two 

 currents in the wattmeter will 

 be = ^ + 03 = 89° 56' 30", 

 and the power factor, cos cf>, 

 of the expression watts = 

 EI cos^will be cos 89°56 / 30" 

 instead of cos 89° 40', that is 

 •00102 instead of '00582; thus 

 the wattmeter would indicate 

 that the power absorbed in the 

 condenser was only about one- 

 sixth of what it really is. If 

 the lag of the shunt-current 

 were more than 20 x (a not 

 improbable value in many 



cases), the deflexion of the wattmeter would be negative ! 

 It is possible that this explains why it has often been claimed 

 that the loss in certain condensers is too small to be measured 

 by a wattmeter. For example, Swinburne*, speaking of 

 some of his own condensers, says " a condenser that takes 

 2000 volts and 10 amperes has a loss that is too low to measure 

 — that is to say, it is less than 5 or 10 watts." 



On the other hand, if by means of a resonance-coil the 

 current and electromotive force have been brought very 

 nearly, if not exactly, into phase, any small lag of the shunt- 

 current will make no appreciable error. Thus, the cosine of 

 10° is -9848, and of 10° 16' 30" is '9840, a difference of less 

 than one part in a thousand. 



In order to determine the precise values of r e and r w a 

 Wheatstone bridge is joined to A D and the condenser short- 

 circuited, so that the resonance-coil and the fixed coil of the 

 wattmeter and the lead-wires form the fourth arm of the 

 bridge. The resistance is then quickly measured just after 

 the wattmeter has been read and the alternating circuit broken, 

 and changes due to temperature are included. 



* < Electrician/ Jan. 1 (1892). 



