The instantaneous voltage v across
the capacitor is
q
v
=C
(7 15)
From the Kirchhoff’s loop rule, the voltage across the source and the
capacitor are equal,
sin
m
q
v
t
C
ω
=
To find the current, we use the relation 
dd
q
i
t
=
(
)
dd
sin
cos(
)
m
m
i
v C
t
C v
t
t
ω
ω
ω
=
=
Using the relation, cos(
)
sin
ω
ω
t
t
=
+

π
2
, we have
i
i
t
=m
+


sin ω
2π
(7 16)
where the amplitude of the oscillating current is im = w Cvm We can rewrite
it as
(1/
)
m
m
v
i
ωC
=
Comparing it to  im= vm/R for a purely resistive circuit, we find that
(1/wC)  plays the role of resistance