Consider an inductor of 2 H with ω = 100 rad/sec and with voltage

v = 10 cos (ωt + 50°) V. The time done current is: 

Concept:

The voltage across the inductor is given by,

\({V_L} = L\frac{{d{i_L}}}{{dt}}\)

\({i_L}\left( t \right) = \frac{1}{L}\smallint {V_L}dt\)

Calculation:

Given V_L(t)=v = 10 cos (ωt + 50°) V

L=2 H ,ω= 100 rad/sec}dt

\({i_L}\left( t \right) = \frac{1}{L}\smallint {V}dt\) 

 ⇒\({i_L}\left( t \right) = \frac{1}{2}\smallint { 10 cos (ωt + 50°)}dt\)

             =0.05 sin (100 t + 50°) A

             =0.05 cos (100 t − 40°) A