Question

Why the rate of change of local terminal current is directly proportional to the inductance as seen by the relay at that terminal

Answer 1

Thee current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance,[1] one arrives at the usual mathematical equation that describes this relationship

{\displaystyle I={\frac {V}{R}},} I={\frac {V}{R}},

where I is the current through the conductor in units of amperes, V is the voltage measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.

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Answer 2

We know that

V = I*X(L )( inductive resistance)

the inductive resistance is constant in terminal so the voltage proportional to the rate current flowing in a conductor .