1
Lecture-17
Resonance in LRC Circuit
•
Forced Harmonic Oscillation
If LRC circuit is driven by
AC source with V
Drive
, then
The current in circuit maximizes when drive
frequency
ω
Drive
equals circuit’s own
ω
LRC
.
Total circuit resistance against the current is at
minimum.
The total circuit resistance, i.e.,
impedance
, can be calculated by “phasors.”
Note
that under steady state condition, rms
values can be used for I, V
R
,
V
L
, V
C
:
V
R
rms
≡
Square Root of
<V
R
2
> ,
where
Thus
V
R rms
≡
I
rms
R
V
L
rms
≡
I
rms
X
L
, where X
L
=
ω
L
V
C
rms
≡
I
rms
X
C
, where X
C
= (
ω
C)
-1
t
V
C
Q
dt
dQ
R
dt
Q
d
L
D
o
ω
sin
2
2
=
+
+
2
2
2
0
2
2
0
2
2
1
)
(
sin
1
)
(
1
2
R
I
dt
t
R
I
T
dt
IR
T
V
o
T
o
T
R
=
=
>=
<
∫
∫
ω

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