When we apply AC to an inductor

[phydis]

"when we apply AC to an inductor (pure inductance), the current will lag the applied voltage by 90 degrees. "

how this happens? why current lags applied voltage by 90 degrees?

 

[facenian]

the equation governing this phenomenon is $v=L\frac{d i}{d t}$ if me put $v(t)=V_{0}cos wt$ an solve the differential equation we get the answer to your question

 

[sophiecentaur]

"when we apply AC to an inductor (pure inductance), the current will lag the applied voltage by 90 degrees. "

how this happens? why current lags applied voltage by 90 degrees?

There is a voltage produced as the current in an inductor changes and that voltage depends upon the rate of change of current. If the current is varying as as cosine, then the rate of change will vary as a sine function.
This is just re-stating the above explanation but avoiding using any explicit Maths, which can bring on the pains for some people. However, calculus is a great way of describing many processes and makes it possible to get more useful answers than words can, on their own.
If the current varies in a more complicated way then the resulting voltage version will not, of course, just be a time-shifted version of the current variation.