15–43 Perfectly Coupled Transformer FigureP15–43isanequivalent circuit ofaperfectlycoupled transformer.

Thismodel is the basis for the transformer equivalent circuits used in the analysis of power systems. The inductanceLm is called the magnetizing inductance. The current through this inductance represents the current needed to establish the magnetic field in the transformer at no load (i2 = 0). Show that the i–v equations for this circuit are as follows

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dis(t) V(t)=Lm +nLm dt di(t) di(1) v2(t)=nLm +nLm dt Use these equations to show that k = 1. dt diz (1) dt i(t) ni(1) i2(t) 1:n V(1) Lm V2(1) Ideal