FUNDAMENTAL PROBLEMS. 69 



28. Resistance, reactance, and impedance. By inspection of 

 Fig. 59 it is seen that the component of E parallel to / is equal 

 to RI* The resistance of an alternating current circuit is in 

 general defined as that factor which multiplied by I gives the 

 component of E parallel to I. In the case discussed above, the 

 resistance of the circuit is the ordinary resistance, R, of the coil 

 shown in Fig. 57. This simple case is the only one that need 

 now be kept in mind, although the definition here given applies 

 to cases to be discussed later, in which the so-called equivalent 

 resistance of an alternating-current circuit is very different from 

 the resistance of the circuit as ordinarily defined, f 



By inspection of Fig. 59 it is seen that the component of E, 

 which is 90 ahead of / in phase, is equal to (&L i/a)C)f. 

 The factor X (= coL i \<*>C\ by which an alternating current 

 is to be multiplied to give the component of E which is po ahead of 

 I in phase, is called the reactance of the alternating current circuit. 

 According to this definition the reactance of the circuit is to be con- 

 sidered as negative if E is behind / in phase. In the case dis- 

 cussed above, the reactance is equal to (coL i/coC), and this 

 simple case is the only one that need now be kept in mind, al- 

 though the definition here given applies to cases to be discussed 

 later, in which the so-called equivalent reactance of an alternating- 

 current circuit is not equal, simply, to ((oL i/a)C.).$ 



By inspecting equation (8) it is seen that the effective value 

 of an alternating electromotive force is equal to the effective 

 value of the current multiplied by the square root of the sum 

 of the squares of the resistance and the reactance of the circuit. 

 The square root of (R 2 -f X 2 ) is called the impedance of the 

 circuit. 



By substituting the value 



* = /;- -I (10) 



o)C 



* See Art. 25, page 62, for a statement as to the representation of effective values 

 in the clock diagram. 



"t See the topic "equivalent resistance " in the index. 

 \ See the topic "equivalent reactance" in the index. 



