Practical Electronics/Parallel LC
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Practical Electronics
Summary
Circuit
Symbol
Series
Parallel
LC
Impedance
Z
Z
t
=
ω
L
+
1
ω
C
=
ω
2
L
C
+
1
ω
C
{\displaystyle Z_{t}=\omega L+{\frac {1}{\omega C}}={\frac {\omega ^{2}LC+1}{\omega C}}}
Z
t
=
ω
L
ω
2
L
C
+
1
{\displaystyle Z_{t}={\frac {\omega L}{\omega ^{2}LC+1}}}
Resonance Frequency
ω
=
ω
o
{\displaystyle \omega =\omega _{o}}
when
Z
L
=
Z
C
{\displaystyle Z_{L}=Z_{C}}
ω
L
=
1
ω
C
{\displaystyle \omega L={\frac {1}{\omega C}}}
ω
o
=
L
C
{\displaystyle \omega _{o}={\sqrt {\frac {L}{C}}}}
ω
L
=
1
ω
C
{\displaystyle \omega L={\frac {1}{\omega C}}}
ω
o
=
L
C
{\displaystyle \omega _{o}={\sqrt {\frac {L}{C}}}}
Voltage
V
V
=
L
d
I
d
t
+
1
C
∫
I
d
t
{\displaystyle V=L{\frac {dI}{dt}}+{\frac {1}{C}}\int Idt}
I
=
1
L
∫
V
d
t
+
C
d
V
d
t
{\displaystyle I={\frac {1}{L}}\int Vdt+C{\frac {dV}{dt}}}
when 
