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Circuits
[
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RC
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Q
(
t
)
=
C
E
(
1
−
e
−
t
R
C
)
=
Q
f
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1
−
e
−
t
R
C
)
{\displaystyle Q(t)=C{\mathcal {E}}\left(1-e^{{}^{-}{\frac {t}{RC}}}\right)=Q_{f}\left(1-e^{{}^{-}{\frac {t}{RC}}}\right)}
I
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t
)
=
E
R
e
−
t
R
C
=
I
0
e
−
t
R
C
{\displaystyle I(t)={\frac {\mathcal {E}}{R}}e^{{}^{-}{\frac {t}{RC}}}=I_{0}e^{{}^{-}{\frac {t}{RC}}}}
RL
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I
(
t
)
=
E
R
(
1
−
e
−
L
R
t
)
=
I
f
(
1
−
e
−
L
R
t
)
{\displaystyle I(t)={\frac {\mathcal {E}}{R}}\left(1-e^{{}^{-}{\frac {L}{R}}t}\right)=I_{f}\left(1-e^{{}^{-}{\frac {L}{R}}t}\right)}
LC
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Q
(
t
)
=
I
0
L
C
sin
t
L
C
+
C
E
=
I
0
L
C
sin
t
L
C
+
Q
0
{\displaystyle Q(t)=I_{0}{\sqrt {LC}}\sin {\frac {t}{\sqrt {LC}}}+C{\mathcal {E}}=I_{0}{\sqrt {LC}}\sin {\frac {t}{\sqrt {LC}}}+Q_{0}}
I
(
t
)
=
I
0
cos
t
L
C
{\displaystyle I(t)=I_{0}\cos {\frac {t}{\sqrt {LC}}}}
