Inductance: Why Does Di/Dt Represent Current?

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Telegrapher's equation from a transmission line model: v(z, t) - R Δz i(z, t) - L Δz ∂i(z, t)/∂t - v(z + Δz, t) = 0.

Circuit schematic of a distributed transmission line segment of length Δz, with series R Δz and L Δz, shunt G Δz and C Δz, labeled with currents i(z, t) and i(z + Δz, t) and voltages v(z, t) and v(z + Δz, t).


why inductance's current represent with di/dt?

ps) and how do you make image big...
 
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Actually the Voltage is Ldi/dt. But I'm not sure that is all you are asking.

A constant voltage across an inductor will cause a constant change in current (di/dt) ... and vice-versa.

No idea about the images, but they expand when people click on them.
 
Make that an Ideal inductor - real inductor's restive elements can have V with no dI/dt... fine for circuit analysis, but in a real circuit this should always be considered.