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