20 BELL SYSTEM TECHNICAL JOURNAL 



equation to (1), we shall have 



L ^ J^ ' + i?(/e-0 = Foe'"'. 



Differentiating and cancelling the time factor e'"', we obtain 



{R + icoL)/ = F. 



The ratio Z = V/I = Fe*"'/-^^""' is called the impedance of the elec- 

 tric circuit. In the present instance 



Z = R + io)L. 



In general, the impedance Z = R -\- iX has a real and an imaginary 

 part, the former being the resistive component of the impedance and 

 the latter the reactive. 



Mechanical Circuits 



Linear oscillations of a mass in a resisting medium are described by 

 equations identical with (1) and (2) except for the customary differ- 

 ence in lettering 



d(ve'"^) , , . ,^ ^ . , 

 m~j — - + r{ve"^^) = Fe'^K 



In this equation, v represents the velocity and F the applied force, 

 m the mass and r the resistance coefficient. The mechanical im- 

 pedance is then 



Z = r -\- icom. «^ 



Similarly, for torsional vibrations the impedance is defined as the 

 ratio "torque/angular velocity." 



Electric Waves in Transmission Lines 



Let X be the distance coordinate specifying a typical section of an 

 electric transmission line. Let the complex quantities F and / be 

 the voltage across and the electric current in the transmission line.^ 

 Then the space rate of change of the voltage is proportional to the 

 current and the space rate of change of the current is proportional to 

 the voltage 



^=-Z/. g=-FF. (2) 



3 The time factor e'"' is usually implicit. 



