Formulae for induced back-EMF
For an inductor V = \$L\dfrac{di}{dt}\$

This is fundamental and always correct. For instance: -


If applied voltage is constant at 1V, current ramps linearly from 0 to infinity at a rate of 1/L amps per second. If L is 0.1 henries it ramps at 10 amps per second
If applied voltage is a 5 Vpk sinewave of 1 radian per second then the differential of current is also a sinewave but with peak value of 5/L
If the differential of current is a sinewave then current is a cosine wave i.e. it lags the voltage by 90 degrees.


Does this help?