In order to calculate the time it takes to charge a certain capacitor with value C at a given constant current of a value I to a voltage of value U, I can use: $$ C = \frac{Q}{U} = \frac{I\Delta t}{U}$$ Is there something equivalent for an Inductor? like: $$ L = \frac{\Phi}{I} = \frac{U\Delta t}{I}$$ I mean, can I calculate the time it takes for a inductor with value L to reach a current I charged with a constant voltage U?
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Yes, you can.
I would write the equations as
$$ C = \frac{I\Delta t}{\Delta U}$$ and $$ L = \frac{U\Delta t}{\Delta I}$$
The second equation is often used to determine the value of the inductor in SMPS using the desired ripple of the current.
Rewriting gives $$ \Delta t = L\frac{\Delta I}{U} $$ which calculates the time it takes to increase the current with \$ \Delta I \$ when a fixed voltage U is applied for a given inductance L.
