INDUCTANCE AND CAPACITY. 



367 



12. Dependence of the capacity of a condenser upon the size 

 and distance apart of its plates. The capacity C of an air con- 

 denser is proportional to the area a of its plates, and inversely 

 proportional to the distance x between its plates, that is C is pro- 

 portional to ajx, or the capacity of a condenser with a given 

 dielectric is proportional to kajx, where k is the inductivity of 

 the dielectric. Indeed the capacity of a condenser may be cal- 

 culated by the equation 



= 885 x 10 



-16 



ka 



(12) 



in which k is the inductivity of the dielectric, x is the thick- 

 ness of the dielectric in centimeters, and a is the area in square 

 centimeters of the dielectric layer between the plates. This 

 equation gives the value of C in farads. 



The capacity of a transmission line, the two wires being con- 

 sidered as the two " plates " of a condenser, is given by the 

 formula 



C __L943JC/ 



in which C is expressed in farads, and /, d and R have the 

 same significance as in equation (8), that is, / is the length of the 

 line in miles. 



13. Mechanical and electrical analogies. The analogy between 

 moment of inertia and inductance as pointed out in the discussion 

 of inductance is but a small part of an extended analogy between 

 pure mechanics and electricity. This extended analogy is here 

 briefly outlined. 



X = Vt (I) 



in which x is the distance 

 traveled in / seconds by a 

 body moving at velocity v. 



in which 



=Fx (4) 

 W is the work 



done by a force F in pull- 



* = * (2} 



in which ty is the angle 

 turned in t seconds by a 

 body turning at angular 

 velocity w. 



W= T$ (5) 

 in which W is the work 

 done by a torque Tin turn- 



q = it (3) 



in which q is the electric 

 charge which in t seconds 

 flows through a circuit car- 

 rying a current i. 



W=Eq (6) 

 in which W is the work 

 done by an electromotive 



