Electricity/Electric circuit/RC circuit
<
Electricity
<
Electric circuit
RC circuit
RC series
v
C
+
v
R
=
0
{\displaystyle v_{C}+v_{R}=0}
C
d
d
t
v
+
v
R
=
0
{\displaystyle C{\frac {d}{dt}}v+{\frac {v}{R}}=0}
d
d
t
v
=
−
1
T
v
{\displaystyle {\frac {d}{dt}}v=-{\frac {1}{T}}v}
v
=
A
e
−
t
T
{\displaystyle v=Ae^{-{\frac {t}{T}}}}
T
=
R
C
{\displaystyle T=RC}
2 port RC
v
o
v
i
=
1
j
ω
C
R
+
1
j
ω
C
=
1
1
+
j
ω
T
{\displaystyle {\frac {v_{o}}{v_{i}}}={\frac {\frac {1}{j\omega C}}{R+{\frac {1}{j\omega C}}}}={\frac {1}{1+j\omega T}}}
T
=
R
C
{\displaystyle T=RC}
ω
o
=
1
T
{\displaystyle \omega _{o}={\frac {1}{T}}}
ω
=
0
{\displaystyle \omega =0}
.
v
o
=
v
i
{\displaystyle v_{o}=v_{i}}
ω
o
=
ω
o
{\displaystyle \omega _{o}=\omega _{o}}
.
v
o
=
v
i
2
{\displaystyle v_{o}={\frac {v_{i}}{2}}}
ω
o
=
00
{\displaystyle \omega _{o}=00}
.
v
o
=
0
{\displaystyle v_{o}=0}
2 port CR
v
o
v
i
=
R
R
+
1
j
ω
C
=
j
ω
T
R
+
j
ω
T
{\displaystyle {\frac {v_{o}}{v_{i}}}={\frac {R}{R+{\frac {1}{j\omega C}}}}={\frac {j\omega T}{R+j\omega T}}}
T
=
R
C
{\displaystyle T=RC}
ω
o
=
1
T
{\displaystyle \omega _{o}={\frac {1}{T}}}
ω
=
0
{\displaystyle \omega =0}
.
v
o
=
0
{\displaystyle v_{o}=0}
ω
o
=
ω
o
{\displaystyle \omega _{o}=\omega _{o}}
.
v
o
=
v
i
2
{\displaystyle v_{o}={\frac {v_{i}}{2}}}
ω
o
=
00
{\displaystyle \omega _{o}=00}
.
v
o
=
v
i
{\displaystyle v_{o}=v_{i}}
. 
. 
. 
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