INDUCTANCES AND RESISTANCES 



square of the number of turns. In Part II of the book we shall return to 

 {[xK^K^)l{KJ). 



Self inductance in series 



If two self inductances are connected in series to a generator whose current 

 changes at a steady rate dijdt {Figure 4.6) the back e.m.f. e^ across L-^ ii 



-= const/ j 



^=-^1 



d/ 

 df 



> --/ d/ 

 ^ ^ d r 



Figure 4.6 



— Li d//d? and across Lg is e^, = — Lg d//d/. The total back e.m.f. is 

 therefore — (Lj + L^ <Mj^t. 



The back e.m.f. across a single coil of the same effective inductance Leff 

 would be e = —Leff d7/d/ 



therefore —Leff d//d/ = — (Lj + Lg) d//d/ 



so Leff = Lj + Lo 



and in general for n self inductances in series Leff = Lj + Lg + L3 . . . + L„. 



Closed a1 '-0 



4 



/ 



Figure 4.7 



Figure 4.8 



Self inductances in parallel 



If a self inductance be connected to a constant direct voltage generator of 

 e.m.f. E {Figure 4.7), the back e.m.f. e must necessarily be equal and opposite 

 to the driving e.m.f. E, E = —e, and 



E = L dZ/d/ 

 therefore 



dijdt =- L/L 



Thus from the instant of closing the switch the current rises from zero 

 towards infinity at a steady rate. If, instead, two self inductances in parallel 

 are connected to the generator {Figure 4.8) then 



dijdt = L/Li 



and dijdt = L/Lg 



d//d/ = dijdt + d/2/d/ = L(l/Li + I/L2) 



57 



so 



