INDUCTANCES AND RESISTANCES 



The rate of rise of current in a single coil of the same self inductance Leff 

 would be EjLeu. 



Therefore EjE^s = ^(1/A + 1/^2) 



and llL,s=llLi+im 



and in general, for n self inductances in parallel, 



11111 



-^eflf El E^ E^ E„ 

 A more convenient form for two self inductances in parallel is 



^''-Ei + E, 



Self inductance connected to constant-voltage alternator 



If a self inductance be connected to a generator of output e = E cos cot 

 {Figure 4.9), there must be an equal and opposite back e.m.f. equal to 

 — E cos cot produced across the inductance. Since this back e.m.f. is also 

 —E dildt, we have 



E di/dt = E cos cot 



therefore / = {.EjE)\ cos cot dt 



= {EjcoE) sin o)t 



Thus the current is also sinusoidal in form, but lagging in phase by 90 degrees 

 on the applied voltage {Figure 4.10). 



i = (ElcoL) sin (ot 



Figure 4.9 Figure 4.10 



The ratio of applied voltage to current, neglecting the phase difference, is 

 the modulus of the inductive reactance, Z^, and is El{EjcoE) — coE. Inductive 

 reactance is conventionally regarded as positive. Thus, iny notation, taking 

 account of the phase difference, the reactance is given by jcoE. 



The power delivered to the inductance per cycle is 



J '277 £2 rz-K 



e . i . dt = — - sin cot . cos cot dt ^= 

 coEJo 



Thus an inductance, like a capachance, consumes no power. Energy surges 

 back and forth between the generator and the magnetic field of the inductance, 

 but none is absorbed. 



Self inductance in series with resistance, connected to constant direct voltage 

 generator 



When an inductance and a resistance are connected in series to a generator 



58 



