different way to find current

https://i28.tinypic.com/2qny713.jpg

they found current by I=e/R

but i thought of finding it in
by e=-LI'

if i integrate I' ill get I
what wrong with that
??

they found current by I=e/R

but i thought of finding it in
by e=-LI'

if i integrate I' ill get I
what wrong with that
??

Click to expand...

Because the e in e=-LI' is not the 500V. The emf across the inductor is changing with time.

The maximum current occurs at steady state when the emf across L is zero. At steady state the entire 500V is across the resistor yielding maximum current.

ok thanks