INDUCTANCES AND RESISTANCES 



This relationship is the basis for transformer action, for we have here an 

 arrangement for transforming one e.m.f. into another which may be higher 

 or lower than it. 



Close at ^^ yv^ 



/--O 



turns turns 



Figure 4.18 



r-^'' 



Figure 4.19 



Tightly coupled mutual inductance connected between constant direct voltage 

 generator and a load resistance 



If now we connect a load resistance to L^ in Figure 4. 18, we get Figure 4. 19. 

 The current through the load resistance R will be E^lR, and the power supplied 

 to it E^jR. This power has to come from the generator, and will be dehvered 

 by it in the form of extra current to Lj. Thus we have 



Extra generator power = Generator voltage X Extra generator current 



or 



therefore 



^zl^ = -£"1 X /o-extra 



'G-extra 



■^■2 E^ JI2 -C-i / 2\ El 



^E^^¥iE^'R~ \nJ R 



Thus, whereas with no load connected the generator supplies a current 

 rising from at the instant of switching on at the rate dZ/dr = EjL (Figure 

 4.20), if a load be connected then on closing the switch the generator current 

 rises instantaneously by an amount (A^2/^i)^ ^il^> ^^^ ^hen continues to 

 rise at the rate EjL (Figure 4.21). 



Slope 



Figure 4.20 



Figure 4.22 



It is clear from the foregoing that the primary current comprises two 

 fractions, a constant one — which represents energy being usefully transferred 

 through to the load — and a steadily rising one — which represents energy 

 being stored in the magnetic field, to no purpose. We therefore introduce 

 the notion of the ideal transformer (Figure 4.22). 



63 



