For an RLC circuit driven with voltage of amplitude vm and frequency
w, we found that the current amplitude is given by
2
2
(
)
m
m
m
C
L
v
v
i
Z
R
X
X
=
=
+
−
with Xc = 1/wC and XL = w L So if w is varied, then at a particular frequency
w0, Xc = XL, and the impedance is minimum (
)
2
02
Z
R
R
=
+
= This
frequency is called the resonant frequency:
0
0
1
or
c
L
X
X
L
C
ω
ω
=
=
or   
0
1
LC
ω
=
(7 28)
At resonant frequency, the current amplitude
is maximum; im = vm/R