To obtain the current, we integrate di/dt with respect to
time:
d
d d
d
ti
t
v
L
t
t
m
∫
∫
=
sin(
)
ω
and get,
cos(
)
constant
vm
i
t
L
= −
ω
+
ω
The integration constant has the dimension of current and is time-
independent Since the source has an emf which oscillates symmetrically
about zero, the current it sustains also oscillates symmetrically about
zero, so that no constant or time-independent component of the current
exists Therefore, the integration constant is zero Using
−
=
−


cos(
)
sin
ω
ω
t
t
2π
, we have
i
i
t
=m
−


sin ω
2π
(7