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Sahib:
To have a zero transient current component in an AC sine wave excited series L-R circuit the applied voltage must be switched on at a phase angle corresponding to where the steady state current would be at 0. 90 degrees is the point for a pure inductor ( R = 0 ). This is true for linear inductor. A non-linear inductor creates a whole different set of conditions.
A saturated ferromagnetic core in a transformer causes a large peak inrush current because the inductance is not a linear item. Inductance drops very low when the core is in saturation. For many magnetic materials saturation is not a square shape. Ordinary transformer material is rather soft. While Permalloy, and Supermalloy are quite square. This change in inductance is all occurring within a portion of one half cycle.
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