s
=
v
⋅
t
[
s
]
=
m
=
m
s
⋅
s
S
t
r
e
c
k
e
=
G
e
s
c
h
w
i
n
d
i
g
k
e
i
t
⋅
Z
e
i
t
{\displaystyle s=v\cdot t\qquad \left[\,s\,\right]=m={m \over s}\cdot s\qquad Strecke=Geschwindigkeit\cdot Zeit}
v
=
c
o
n
s
t
.
G
e
s
c
h
w
i
n
d
i
g
k
e
i
t
{\displaystyle v=const.\qquad Geschwindigkeit}
F
=
0
K
r
a
f
t
e
i
n
w
i
r
k
u
n
g
a
u
f
d
i
e
M
a
s
s
e
{\displaystyle F=0\qquad Krafteinwirkung\ auf\ die\ Masse}
a
=
0
B
e
s
c
h
l
e
u
n
i
g
u
n
g
{\displaystyle a=0\qquad Beschleunigung}
s
=
1
2
⋅
a
⋅
t
2
[
s
]
=
m
=
m
s
2
⋅
s
2
S
t
r
e
c
k
e
=
1
2
⋅
B
e
s
c
h
l
e
u
n
i
g
u
n
g
⋅
Z
e
i
t
2
{\displaystyle s={1 \over 2}\cdot a\cdot t^{2}\qquad \left[\,s\,\right]=m={m \over s^{2}}\cdot s^{2}\qquad Strecke={1 \over 2}\cdot Beschleunigung\cdot Zeit^{2}}
v
=
a
⋅
t
[
v
]
=
m
s
=
m
s
2
⋅
s
G
e
s
c
h
w
i
n
d
i
g
k
e
i
t
=
B
e
s
c
h
l
e
u
n
g
f
i
g
u
n
g
⋅
Z
e
i
t
{\displaystyle v=a\cdot t\qquad \left[\,v\,\right]={m \over s}={m \over s^{2}}\cdot s\qquad Geschwindigkeit=Beschleungfigung\cdot Zeit}
F
=
m
⋅
a
[
F
]
=
N
=
k
g
⋅
m
s
2
K
r
a
f
t
=
M
a
s
s
e
⋅
B
e
s
c
h
l
e
u
n
i
g
u
n
g
{\displaystyle F=m\cdot a\qquad \left[\,F\,\right]=N=kg\cdot {m \over s^{2}}\qquad Kraft=Masse\cdot Beschleunigung}
a
=
c
o
n
s
t
.
{\displaystyle a=const.}
v
=
s
˙
{\displaystyle v={\dot {s}}}
a
=
v
˙
=
s
¨
{\displaystyle a={\dot {v}}={\ddot {s}}}
E
P
o
t
=
m
⋅
g
⋅
h
[
E
P
o
t
]
=
J
=
k
g
⋅
m
s
2
⋅
m
E
n
e
r
g
i
e
=
M
a
s
s
e
⋅
E
r
d
b
e
s
c
h
l
.
⋅
H
o
e
h
e
{\displaystyle E_{Pot}=m\cdot g\cdot h\quad \left[\,E_{Pot}\,\right]=J=kg\cdot {m \over s^{2}}\cdot m\quad Energie=Masse\cdot Erdbeschl.\cdot Hoehe}
E
K
i
n
=
1
2
⋅
m
⋅
v
2
[
E
K
i
n
]
=
J
=
k
g
⋅
(
m
s
)
2
E
n
e
r
g
i
e
=
1
2
⋅
M
a
s
s
e
⋅
G
e
s
c
h
w
.
2
{\displaystyle E_{Kin}={1 \over 2}\cdot m\cdot v^{2}\quad \left[\,E_{Kin}\,\right]=J=kg\cdot \left({m \over s}\right)^{2}\quad Energie={1 \over 2}\cdot Masse\cdot Geschw.^{2}}
E
S
p
a
n
n
=
1
2
⋅
D
⋅
s
2
[
E
S
p
a
n
n
]
=
J
=
N
m
⋅
m
2
E
n
.
=
1
2
⋅
F
e
d
e
r
k
o
n
s
t
.
⋅
S
t
r
e
c
k
e
2
{\displaystyle E_{Spann}={1 \over 2}\cdot D\cdot s^{2}\quad \left[\,E_{Spann}\,\right]=J={N \over m}\cdot m^{2}\quad En.={1 \over 2}\cdot Federkonst.\cdot Strecke^{2}}
D
=
F
s
[
D
]
=
N
m
=
k
g
⋅
m
s
e
c
2
m
F
e
d
e
r
k
o
n
s
t
a
n
t
e
=
K
r
a
f
t
S
r
e
c
k
e
{\displaystyle D={F \over s}\quad \left[\,D\,\right]={N \over m}={{kg\cdot m \over sec^{2}} \over m}\quad Federkonstante={Kraft \over Srecke}}
p
→
=
m
⋅
v
→
[
p
]
=
k
g
⋅
m
s
I
m
p
u
l
s
=
M
a
s
s
e
⋅
G
e
s
c
h
w
i
n
d
i
g
k
e
i
t
{\displaystyle {\overrightarrow {p}}=m\cdot {\overrightarrow {v}}\qquad \left[\,p\,\right]=kg\cdot {m \over s}\qquad Impuls=Masse\cdot Geschwindigkeit}
Es gilt die Impulserhaltung! Ohne Reibung bleibt der Impuls vollständig erhalten!
F
Z
=
m
⋅
r
⋅
ω
2
=
m
⋅
v
2
r
[
F
Z
]
=
N
=
k
g
⋅
(
m
s
)
2
m
K
r
a
f
t
=
M
a
s
s
e
⋅
G
e
s
c
h
w
.
2
R
a
d
i
u
s
{\displaystyle F_{Z}=m\cdot r\cdot \omega ^{2}={m\cdot v^{2} \over r}\quad \left[\,F_{Z}\,\right]=N={kg\cdot \left({m \over s}\right)^{2} \over m}\quad Kraft={Masse\cdot Geschw.^{2} \over Radius}}
ω
=
2
π
⋅
f
=
2
π
T
[
ω
]
=
1
s
W
i
n
k
e
l
g
e
s
c
h
w
.
=
2
π
⋅
U
m
l
.
F
r
e
q
u
e
n
z
=
2
π
U
m
l
a
u
f
z
e
i
t
{\displaystyle \omega =2\pi \cdot f={2\pi \over T}\quad \left[\,\omega \,\right]={1 \over s}\quad Winkelgeschw.=2\pi \cdot Uml.Frequenz={2\pi \over Umlaufzeit}}
L
=
r
⋅
p
⊥
[
L
]
=
m
⋅
k
g
⋅
m
s
e
c
=
J
⋅
s
e
c
D
r
e
h
i
m
p
u
l
s
=
R
a
d
i
u
s
⋅
S
e
n
k
r
.
I
m
p
u
l
s
{\displaystyle L=r\cdot p_{\bot }\qquad \left[\,L\,\right]=m\cdot {kg\cdot m \over sec}=J\cdot sec\qquad Drehimpuls=Radius\cdot Senkr.Impuls}
L
=
r
⋅
m
⋅
v
[
L
]
=
m
⋅
k
g
⋅
m
s
e
c
=
N
m
⋅
s
e
c
=
J
⋅
s
e
c
{\displaystyle L=r\cdot m\cdot v\qquad \left[\,L\,\right]=m\cdot kg\cdot {m \over sec}=Nm\cdot sec=J\cdot sec}
D
r
e
h
i
m
p
u
l
s
=
R
a
d
i
u
s
⋅
M
a
s
s
e
⋅
G
e
s
c
h
w
i
n
d
i
g
k
e
i
t
{\displaystyle Drehimpuls=Radius\cdot Masse\cdot Geschwindigkeit}
I
=
=
Q
t
[
I
=
]
=
C
o
u
l
s
e
c
S
t
r
o
m
=
L
a
d
u
n
g
Z
e
i
t
{\displaystyle I_{=}={Q \over t}\qquad \left[\,I_{=}\,\right]={Coul \over sec}\qquad Strom={Ladung \over Zeit}}
I
≈
=
Q
˙
=
d
q
d
t
[
I
≈
]
=
C
o
u
l
s
e
c
S
t
r
o
m
=
L
a
d
u
n
g
s
d
i
f
f
.
Z
e
i
t
d
i
f
f
.
{\displaystyle I_{\approx }={\dot {Q}}={dq \over dt}\qquad \left[\,I_{\approx }\,\right]={Coul \over sec}\qquad Strom={Ladungsdiff. \over Zeitdiff.}}
U
=
W
q
[
U
]
=
V
=
J
C
o
u
l
=
N
⋅
m
C
o
u
l
S
p
a
n
n
u
n
g
=
A
r
b
e
i
t
L
a
d
u
n
g
{\displaystyle U={W \over q}\qquad \left[\,U\,\right]=V={J \over Coul}={N\cdot m \over Coul}\qquad Spannung={Arbeit \over Ladung}}
R
=
U
I
[
R
]
=
Ω
=
V
A
W
i
d
e
r
s
t
a
n
d
=
S
p
a
n
n
u
n
g
S
t
r
o
m
{\displaystyle R={U \over I}\qquad \left[\,R\,\right]=\Omega ={V \over A}\qquad Widerstand={Spannung \over Strom}}
R
G
e
s
=
R
1
+
R
2
+
.
.
.
+
R
n
=
∑
n
=
1
n
R
n
{\displaystyle R_{Ges}=R_{1}+R_{2}+...+R_{n}=\sum _{n=1}^{n}R_{n}}
U
G
e
s
=
U
1
+
U
2
+
.
.
.
+
U
n
{\displaystyle U_{Ges}=U_{1}+U_{2}+...+U_{n}}
I
G
e
s
=
I
1
=
I
2
=
.
.
.
=
I
n
{\displaystyle I_{Ges}=I_{1}=I_{2}=...=I_{n}}
1
R
G
e
s
=
1
R
1
+
1
R
2
+
.
.
.
+
1
R
n
=
∑
n
=
1
n
1
R
n
{\displaystyle {1 \over R_{Ges}}={1 \over R_{1}}+{1 \over R_{2}}+...+{1 \over R_{n}}=\sum _{n=1}^{n}{1 \over R_{n}}}
U
G
e
s
=
U
1
=
U
2
=
.
.
.
=
U
n
{\displaystyle U_{Ges}=U_{1}=U_{2}=...=U_{n}}
I
G
e
s
=
I
1
+
I
2
+
.
.
.
+
I
n
m
i
t
I
1
I
2
=
R
2
R
1
{\displaystyle I_{Ges}=I_{1}+I_{2}+...+I_{n}\quad mit\quad {I_{1} \over I_{2}}={R_{2} \over R_{1}}}
P
=
U
⋅
I
[
P
]
=
W
=
V
⋅
A
=
J
s
=
N
⋅
m
s
L
e
i
s
t
u
n
g
=
S
p
a
n
n
u
n
g
⋅
S
t
r
o
m
{\displaystyle P=U\cdot I\qquad \left[\,P\,\right]=W=V\cdot A={J \over s}={N\cdot m \over s}\qquad Leistung=Spannung\cdot Strom}
W
=
P
⋅
t
[
W
]
=
J
=
W
a
t
t
⋅
s
e
c
A
r
b
e
i
t
=
L
e
i
s
t
u
n
g
⋅
Z
e
i
t
=
U
⋅
I
⋅
t
[
W
]
=
J
=
V
⋅
A
⋅
s
e
c
=
S
t
r
o
m
⋅
S
p
a
n
n
u
n
g
⋅
Z
e
i
t
{\displaystyle {\begin{matrix}W&=&P\cdot t&&[\,W\,]=J=Watt\cdot sec&&Arbeit&=&Leistung\cdot Zeit\\\ &=&U\cdot I\cdot t&&[\,W\,]=J=V\cdot A\cdot sec\ &&\ &=&Strom\cdot Spannung\cdot Zeit\end{matrix}}}
E
→
=
F
e
→
Q
[
E
→
]
=
N
C
o
u
l
E
l
e
k
t
r
.
F
e
l
d
=
K
r
a
f
t
L
a
d
u
n
g
{\displaystyle {\overrightarrow {E}}={{\overrightarrow {F_{e}}} \over Q}\qquad \left[\,{\overrightarrow {E}}\,\right]=\,{N \over Coul}\qquad Elektr.Feld={Kraft \over Ladung}}
F
C
o
u
l
=
1
4
π
ϵ
0
ϵ
r
⋅
Q
⋅
q
r
2
[
F
C
o
u
l
]
=
N
=
1
F
a
r
m
⋅
C
o
u
l
⋅
C
o
u
l
m
2
K
r
a
f
t
=
c
o
n
s
t
.
⋅
L
a
d
1
⋅
L
a
d
2
A
b
s
t
a
n
d
2
.
{\displaystyle F_{Coul}={1 \over 4\pi \epsilon _{0}\epsilon _{r}}\cdot {Q\!\cdot \!q \over r^{2}}\quad \left[\,F_{Coul}\,\right]=N={1 \over {Far \over m}}\cdot {Coul\cdot Coul \over m^{2}}\quad Kraft=const.\cdot {Lad_{1}\cdot Lad_{2} \over Abstand^{2}.}}
E
=
U
d
[
E
]
=
N
c
o
u
l
=
V
m
E
l
e
k
t
r
.
F
e
l
d
=
S
p
a
n
n
u
n
g
P
l
a
t
t
e
n
a
b
s
t
.
{\displaystyle E={U \over d}\qquad \left[\,E\,\right]={N \over coul}={V \over m}\qquad Elektr.Feld={Spannung \over Plattenabst.}}
Elektrische Feldkraft im Plattenkondensator
Bearbeiten
F
F
e
l
d
=
q
⋅
E
→
=
q
⋅
U
d
[
F
F
e
l
d
]
=
N
=
C
o
u
l
⋅
N
C
o
u
l
=
C
o
u
l
⋅
V
m
K
r
a
f
t
=
L
a
d
u
n
g
⋅
S
p
a
n
n
u
n
g
P
l
a
t
t
e
n
a
b
s
t
.
{\displaystyle F_{Feld}=q\cdot {\overrightarrow {E}}=q\cdot {U \over d}\quad \left[F_{Feld}\right]=N=Coul\cdot {N \over Coul}=Coul\cdot {V \over m}\quad Kraft=Ladung\cdot {Spannung \over Plattenabst.}}
σ
=
Q
A
[
σ
]
=
C
o
u
l
m
2
S
i
g
m
a
=
L
a
d
u
n
g
F
l
a
e
c
h
e
{\displaystyle \sigma ={Q \over A}\qquad \left[\,\sigma \,\right]={Coul \over m^{2}}\qquad Sigma={Ladung \over Flaeche}}
C
=
Q
U
[
C
]
=
F
a
r
=
C
o
u
l
V
K
a
p
a
z
i
t
a
e
t
=
L
a
d
u
n
g
S
p
a
n
n
u
n
g
{\displaystyle C={Q \over U}\qquad \left[\,C\,\right]=Far={Coul \over V}\qquad Kapazitaet={Ladung \over Spannung}}
C
=
ϵ
r
⋅
ϵ
0
⋅
A
d
[
C
]
=
F
a
r
=
1
⋅
A
s
e
c
V
m
⋅
m
2
m
K
a
p
a
z
i
t
a
e
t
=
ϵ
r
⋅
ϵ
0
⋅
F
l
a
e
c
h
e
A
b
s
t
a
n
d
{\displaystyle C=\epsilon _{r}\cdot \epsilon _{0}\cdot {A \over d}\qquad \left[\,C\,\right]=Far=1\cdot {Asec \over Vm}\cdot {m^{2} \over m}\qquad Kapazitaet=\epsilon _{r}\cdot \epsilon _{0}\cdot {Flaeche \over Abstand}}
U
(
t
)
=
U
0
⋅
e
−
a
⋅
t
{\displaystyle U(t)=U_{0}\cdot e^{-a\cdot t}}
a
=
ln
k
Δ
t
k
=
U
1
U
0
=
U
2
U
1
=
.
.
.
{\displaystyle a={\ln k \over \Delta t}\qquad k={U_{1} \over U_{0}}={U_{2} \over U_{1}}=...}
n sind Werte zu verschiedenen Zeiten, die alle den selben Zeitabstand voneinander haben müssen
E
K
o
n
=
1
2
⋅
C
⋅
U
2
[
E
K
o
n
]
=
J
=
F
a
r
⋅
V
2
E
n
e
r
g
i
e
=
1
2
⋅
K
a
p
a
z
i
t
a
e
t
⋅
S
p
a
n
n
u
n
g
2
{\displaystyle E_{Kon}={1 \over 2}\cdot C\cdot U^{2}\quad \left[\,E_{Kon}\,\right]=J=Far\cdot V^{2}\quad Energie={1 \over 2}\cdot Kapazitaet\cdot Spannung^{2}}
C
g
e
s
=
C
1
+
C
2
+
.
.
.
+
C
n
=
∑
n
=
1
n
C
n
{\displaystyle C_{ges}=C_{1}+C_{2}+...+C_{n}=\sum _{n=1}^{n}C_{n}}
1
C
g
e
s
=
1
C
1
+
1
C
2
+
.
.
.
+
1
C
n
=
∑
n
=
1
n
1
C
n
{\displaystyle {1 \over C_{ges}}={1 \over C_{1}}+{1 \over C_{2}}+...+{1 \over C_{n}}=\sum _{n=1}^{n}{1 \over C_{n}}}
U
I
n
d
=
−
n
⋅
Φ
˙
[
U
I
n
d
]
=
V
I
n
d
u
n
k
t
i
o
n
=
−
W
i
n
d
u
g
s
z
a
h
l
⋅
Φ
˙
{\displaystyle U_{Ind}=-n\cdot {\dot {\Phi }}\qquad \left[\,U_{Ind}\,\right]=V\qquad Indunktion=-Windugszahl\cdot {\dot {\Phi }}}
Φ
=
A
⋅
B
[
Φ
]
=
m
2
⋅
T
S
p
u
l
e
n
q
u
e
r
s
c
h
n
i
t
t
s
f
l
a
e
c
h
e
⋅
M
a
g
n
e
t
f
e
l
d
{\displaystyle \Phi =A\cdot B\qquad \left[\,\Phi \,\right]=m^{2}\cdot T\qquad Spulenquerschnittsflaeche\cdot Magnetfeld}
Φ
˙
=
A
˙
⋅
B
+
A
⋅
B
˙
[
Φ
˙
]
=
m
2
⋅
T
s
e
c
{\displaystyle {\dot {\Phi }}={\dot {A}}\cdot B+A\cdot {\dot {B}}\qquad \qquad \qquad \left[\,{\dot {\Phi }}\,\right]={m^{2}\cdot T \over sec}}
U
I
n
d
S
e
l
b
s
t
=
−
L
⋅
I
˙
[
U
]
=
V
=
H
e
n
r
y
⋅
A
s
e
c
S
p
.
=
−
I
n
d
u
k
t
.
⋅
S
t
r
o
m
a
e
n
d
e
r
u
n
g
{\displaystyle U_{Ind_{Selbst}}=-L\cdot {\dot {I}}\quad \left[\,U\,\right]=V=Henry\cdot {A \over sec}\quad Sp.=-Indukt.\cdot Stromaenderung}
L
=
μ
0
⋅
μ
r
⋅
A
⋅
n
2
l
[
L
]
=
H
e
n
r
y
=
V
⋅
s
e
c
A
{\displaystyle L={\frac {\mu _{0}\cdot \mu _{r}\cdot A\cdot n^{2}}{l}}\qquad \left[\,L\,\right]=Henry={V\cdot sec \over A}}
2 , l=Laenge der Spule in m, n=Windungszahl
B
S
p
u
l
e
=
μ
0
⋅
μ
r
⋅
n
⋅
I
l
[
B
S
p
]
=
T
=
N
A
m
F
l
u
s
s
d
.
=
μ
0
⋅
μ
r
⋅
W
i
n
d
.
z
a
h
l
⋅
S
t
r
o
m
S
p
u
l
e
n
l
a
e
n
g
e
{\displaystyle B_{Spule}=\mu _{0}\cdot \mu _{r}\cdot {n\cdot I \over l}\qquad \left[\,B_{Sp}\,\right]=T={N \over Am}\qquad Flussd.=\mu _{0}\cdot \mu _{r}\cdot {Wind.zahl\cdot Strom \over Spulenlaenge}}
E
S
p
u
l
e
=
1
2
⋅
L
⋅
I
2
[
E
S
p
u
l
e
]
=
J
=
H
e
n
r
y
⋅
A
2
E
n
e
r
g
i
e
=
1
2
⋅
S
e
l
b
s
t
I
n
d
.
⋅
S
t
r
o
m
2
{\displaystyle E_{Spule}={1 \over 2}\cdot L\cdot I^{2}\qquad \left[\,E_{Spule}\,\right]=J=Henry\cdot A^{2}\qquad Energie={1 \over 2}\cdot SelbstInd.\cdot Strom^{2}}
B
→
=
F
m
→
I
⋅
l
⊥
→
[
B
]
=
T
=
N
A
⋅
m
F
l
u
s
s
d
i
c
h
t
e
=
M
a
g
n
.
K
r
a
f
t
S
t
r
o
m
⋅
L
a
e
n
g
e
{\displaystyle {\overrightarrow {B}}={{\overrightarrow {F_{m}}} \over I\cdot {\overrightarrow {l_{\bot }}}}\qquad \left[\,B\,\right]=T={N \over A\cdot m}\qquad Flussdichte={Magn.Kraft \over Strom\cdot Laenge}}
F
m
→
=
B
→
⋅
I
⋅
l
⊥
→
{\displaystyle {\overrightarrow {F_{m}}}={\overrightarrow {B}}\cdot I\cdot {\overrightarrow {l_{\bot }}}}
F
L
=
Q
⋅
v
⋅
B
⊥
[
F
L
]
=
N
=
c
o
u
l
⋅
m
s
e
c
⋅
T
K
r
a
f
t
=
L
a
d
.
⋅
G
e
s
c
h
w
.
⋅
S
e
n
k
r
.
M
−
F
e
l
d
{\displaystyle F_{L}=Q\cdot v\cdot B_{\bot }\quad \left[\,F_{L}\,\right]=N=coul\cdot {m \over sec}\cdot T\quad Kraft=Lad.\cdot Geschw.\cdot Senkr.M\!-\!Feld}
U
H
=
d
⋅
v
⋅
B
⊥
[
U
H
]
=
V
=
m
⋅
m
s
e
c
⋅
T
S
p
.
=
P
l
a
e
t
t
c
h
.
b
r
e
i
t
e
⋅
G
e
s
c
h
w
.
⋅
S
e
n
k
r
.
M
−
F
e
l
d
{\displaystyle U_{H}=d\cdot v\cdot B_{\bot }\quad \left[\,U_{H}\,\right]=V=m\cdot {m \over sec}\cdot T\quad Sp.=Plaettch.breite\cdot Geschw.\cdot Senkr.M\!-\!Feld}
U
(
t
)
=
U
^
⋅
sin
(
ω
⋅
t
)
s
i
n
u
s
f
o
e
r
m
i
g
e
S
p
a
n
n
u
n
g
{\displaystyle \operatorname {U} (t)={\hat {U}}\cdot \sin(\omega \cdot t)\qquad \qquad sinusfoermige\ Spannung}
U
^
=
n
⋅
B
⋅
A
⋅
ω
[
U
]
=
V
=
1
⋅
T
⋅
m
2
⋅
1
s
e
c
{\displaystyle {\hat {U}}=n\cdot B\cdot A\cdot \omega \qquad \left[\,U\,\right]=V=1\cdot T\cdot m^{2}\cdot {1 \over sec}}
W
i
n
d
u
n
g
s
z
a
h
l
⋅
B
−
F
e
l
d
⋅
S
p
u
l
e
n
q
u
e
r
s
c
h
n
i
t
t
s
f
l
a
e
c
h
e
⋅
W
i
n
k
e
l
g
e
s
c
h
w
i
n
d
i
g
k
e
i
t
{\displaystyle Windungszahl\cdot B\!-\!Feld\cdot Spulenquerschnittsflaeche\cdot Winkelgeschwindigkeit}
Gilt nur für sinusförmige Wechselspannung!
U
e
f
f
=
U
^
2
I
e
f
f
=
I
^
2
{\displaystyle U_{eff}={{\hat {U}} \over {\sqrt {2}}}\qquad \qquad \qquad I_{eff}={{\hat {I}} \over {\sqrt {2}}}}
Z
=
U
e
f
f
I
e
f
f
{\displaystyle Z={U_{eff} \over I_{eff}}}
R
C
=
1
ω
⋅
C
[
R
C
]
=
Ω
W
i
d
e
r
s
t
a
n
d
=
ω
⋅
1
W
i
n
k
e
l
g
e
s
c
h
w
.
⋅
K
a
p
a
z
i
t
a
e
t
{\displaystyle R_{C}={1 \over \omega \cdot C}\qquad \left[\,R_{C}\,\right]=\Omega \qquad Widerstand=\omega \cdot {1 \over Winkelgeschw.\cdot Kapazitaet}}
R
L
=
ω
⋅
L
[
R
L
]
=
Ω
W
i
d
e
r
s
t
a
n
d
=
W
i
n
k
e
l
g
e
s
c
h
w
.
⋅
S
e
l
b
s
t
i
n
d
.
{\displaystyle R_{L}=\omega \cdot L\qquad \left[\,R_{L}\,\right]=\Omega \qquad Widerstand=Winkelgeschw.\cdot Selbstind.}
ω
=
2
π
⋅
f
=
2
π
T
[
ω
]
=
1
s
W
i
n
k
e
l
g
e
s
c
h
w
.
=
2
π
⋅
U
m
l
.
F
r
e
q
u
e
n
z
=
2
π
U
m
l
a
u
f
z
e
i
t
{\displaystyle \omega =2\pi \cdot f={2\pi \over T}\qquad \left[\,\omega \,\right]={1 \over s}\qquad Winkelgeschw.=2\pi \cdot Uml.Frequenz={2\pi \over Umlaufzeit}}
Reihenschaltung aus ohmischem Wiederstand R, induktivem Blindwiederstand
ω
L
{\displaystyle \omega L}
1
ω
C
{\displaystyle {1 \over \omega C}}
ω
{\displaystyle \omega }
Z
=
R
2
+
(
ω
⋅
L
−
1
ω
⋅
C
)
2
{\displaystyle Z={\sqrt {R^{2}+\left(\,\omega \cdot L-{1 \over \omega \cdot C}\,\right)^{2}}}}
I
e
f
f
=
U
e
f
f
R
2
+
(
ω
⋅
L
−
1
ω
⋅
C
)
2
{\displaystyle I_{eff}={U_{eff} \over {\sqrt {R^{2}+\left(\,\omega \cdot L-{1 \over \omega \cdot C}\,\right)^{2}}}}}
X
=
ω
⋅
L
−
1
ω
⋅
C
{\displaystyle X=\omega \cdot L-{1 \over \omega \cdot C}}
I
(
t
)
=
I
^
⋅
sin
(
ω
t
−
α
)
{\displaystyle \operatorname {I} \,(t)={\hat {I}}\cdot \sin \,(\omega t-\alpha )}
U
(
t
)
=
U
^
⋅
sin
(
ω
t
)
{\displaystyle \operatorname {U} \,(t)={\hat {U}}\cdot \sin \,(\omega t)}
α
{\displaystyle \alpha }
tan
α
=
X
R
=
ω
⋅
L
−
1
ω
⋅
C
R
{\displaystyle \tan \alpha ={X \over R}={\omega \cdot L-{1 \over \omega \cdot C} \over R}}
α
>
0
{\displaystyle \alpha >0}
I
(
t
)
{\displaystyle \operatorname {I} (t)}
U
(
t
)
{\displaystyle \operatorname {U} (t)}
α
<
0
{\displaystyle \alpha <0}
P
w
i
r
k
=
U
e
f
f
⋅
I
e
f
f
⋅
cos
(
α
)
[
P
w
i
r
k
]
=
V
⋅
A
=
J
s
{\displaystyle P_{wirk}=U_{eff}\cdot I_{eff}\cdot \cos(\alpha )\qquad \left[\,P_{wirk}\,\right]=V\cdot A={J \over s}}
W
i
r
k
l
e
i
s
t
u
n
g
=
E
f
f
.
S
p
a
n
n
u
n
g
⋅
E
f
f
.
S
t
r
o
m
⋅
cos
(
P
h
a
s
e
n
w
i
n
k
e
l
)
{\displaystyle Wirkleistung=Eff.Spannung\cdot Eff.Strom\cdot \cos(Phasenwinkel)}
F
R
u
e
c
k
∼
−
s
{\displaystyle F_{Rueck}\sim -s}
F
R
u
e
c
k
=
−
D
⋅
s
[
F
R
u
e
c
k
]
=
N
=
N
m
⋅
m
K
r
a
f
t
=
−
F
e
d
e
r
k
o
n
s
t
a
n
t
e
⋅
S
t
r
e
c
k
e
{\displaystyle F_{Rueck}=-D\cdot s\qquad \left[\,F_{Rueck}\,\right]=N={N \over m}\cdot m\qquad Kraft=-Federkonstante\cdot Strecke}
T
=
2
⋅
π
⋅
l
g
S
c
h
w
.
D
a
u
e
r
=
2
⋅
π
⋅
L
a
e
n
g
e
E
r
d
a
n
z
i
e
h
u
n
g
s
k
o
n
s
t
a
n
t
e
{\displaystyle T=2\cdot \pi \cdot {\sqrt {l \over g}}\qquad Schw.Dauer=2\cdot \pi \cdot {\sqrt {Laenge \over Erdanziehungskonstante}}}
T
=
2
⋅
π
⋅
m
D
S
c
h
w
.
D
a
u
e
r
=
2
⋅
π
⋅
M
a
s
s
e
F
e
d
e
r
k
o
n
s
t
a
n
t
e
{\displaystyle T=2\cdot \pi \cdot {\sqrt {m \over D}}\qquad Schw.Dauer=2\cdot \pi \cdot {\sqrt {Masse \over Federkonstante}}}
T
=
2
⋅
π
⋅
l
2
⋅
g
S
c
h
w
.
D
a
u
e
r
=
2
⋅
π
⋅
L
a
e
n
g
e
d
.
W
a
s
s
e
r
s
a
e
u
l
e
2
⋅
G
r
a
v
i
t
a
t
i
o
n
s
k
o
n
s
t
a
n
t
e
{\displaystyle T=2\cdot \pi \cdot {\sqrt {l \over 2\cdot g}}\qquad Schw.Dauer=2\cdot \pi \cdot {\sqrt {Laenge\ d.Wassersaeule \over 2\cdot Gravitationskonstante}}}
s
(
t
)
=
S
0
⋅
e
a
⋅
t
⋅
cos
(
ω
⋅
t
)
{\displaystyle \operatorname {s} \,(t)=S_{0}\cdot e^{a\cdot t}\cdot \cos \,(\omega \cdot t)}
c
=
λ
⋅
f
[
c
]
=
m
s
e
c
=
m
⋅
1
s
e
c
G
e
s
c
h
w
.
=
W
e
l
l
e
n
l
.
⋅
F
r
e
q
u
e
n
z
{\displaystyle c=\lambda \cdot f\qquad \left[\,c\,\right]={m \over sec}=m\cdot {1 \over sec}\qquad Geschw.=Wellenl.\cdot Frequenz}
s
h
i
n
(
t
,
x
)
=
s
^
⋅
sin
[
2
⋅
π
⋅
(
t
T
−
x
λ
)
]
{\displaystyle \operatorname {s_{hin}} \,(t,\,x)={\hat {s}}\cdot \sin \,\left[\,2\cdot \pi \cdot \left(\,{t \over T}-{x \over \lambda }\,\right)\,\right]}
s
r
u
e
c
k
l
o
s
e
(
t
,
x
)
=
+
s
^
⋅
sin
[
2
⋅
π
⋅
(
t
T
+
x
λ
)
]
{\displaystyle \operatorname {s_{rueck_{lose}}} \,(t,\,x)=\mathbf {+} {\hat {s}}\cdot \sin \,\left[\,2\cdot \pi \cdot \left(\,{t \over T}\mathbf {+} {x \over \lambda }\,\right)\,\right]}
s
r
u
e
c
k
f
e
s
t
(
t
,
x
)
=
−
s
^
⋅
sin
[
2
⋅
π
⋅
(
t
T
+
x
λ
)
]
{\displaystyle \operatorname {s_{rueck_{fest}}} \,(t,\,x)={\mathit {\mathbf {-} }}{\hat {s}}\cdot \sin \,\left[\,2\cdot \pi \cdot \left(\,{t \over T}\mathbf {+} {x \over \lambda }\,\right)\,\right]}
s
(
t
,
x
)
=
s
h
i
n
(
t
,
x
)
+
s
r
u
e
c
k
l
o
s
e
(
t
,
x
)
{\displaystyle \operatorname {s} \,(t,\,x)=\operatorname {s_{hin}} \,(t,\,x)+\operatorname {s_{rueck_{lose}}} \,(t,\,x)}
Intensität = (Amplitude)2
sin
(
α
)
=
g
a
sin
(
B
e
o
b
a
c
h
t
u
n
g
s
w
i
n
k
e
l
)
=
G
a
n
g
u
n
t
e
r
s
c
h
i
e
d
S
p
a
l
t
a
b
s
t
a
n
d
{\displaystyle \sin \,(\alpha )={g \over a}\qquad \sin(Beobachtungswinkel)={Gangunterschied \over Spaltabstand}}
λ
{\displaystyle \lambda }
λ
2
{\displaystyle {\lambda \over 2}}
n
=
sin
(
α
)
sin
(
β
)
{\displaystyle n={\sin \,(\alpha ) \over \sin \,(\beta )}}
α
{\displaystyle \alpha }
β
{\displaystyle \beta }
sin
(
α
)
sin
(
β
)
=
c
1
c
2
=
n
2
n
1
{\displaystyle {\sin(\alpha ) \over \sin(\beta )}={c_{1} \over c_{2}}={n_{2} \over n_{1}}}
2
d
⋅
sin
ϕ
=
λ
,
2
λ
,
3
λ
,
.
.
.
d
=
A
b
s
t
a
n
d
z
w
.
d
e
n
G
i
t
t
e
r
e
b
e
n
e
n
{\displaystyle \mathrm {2} d\cdot \sin \phi \mathrm {\ =\ } \lambda {,}\ \mathrm {2} \lambda {,}\ \mathrm {3} \lambda {,}\ \mathrm {...} \qquad d\ \mathrm {=} \ \mathrm {Abstand\ zw.\ den\ Gitterebenen} }
W
p
h
o
t
=
h
⋅
f
[
W
P
h
o
t
]
=
J
=
J
⋅
s
⋅
H
z
=
J
⋅
s
⋅
1
s
{\displaystyle W_{phot}=h\cdot f\qquad \left[\,W_{Phot}\,\right]=J=J\cdot s\cdot Hz=J\cdot s\cdot {1 \over s}}
E
n
e
r
g
i
e
=
P
l
a
n
c
k
′
s
c
h
e
K
o
n
s
t
.
⋅
F
r
e
q
u
e
n
z
{\displaystyle \mathrm {Energie=\ Planck'sche\,Konst.\ \cdot \ Frequenz} }
W
e
−
=
W
p
h
o
t
=
e
⋅
U
=
h
⋅
f
m
a
x
[
W
e
−
]
=
J
=
c
o
u
l
⋅
V
=
h
⋅
H
z
{\displaystyle W_{e^{-}}=W_{phot}=e\cdot U=h\cdot f_{max}\quad \left[\,W_{e^{-}}\,\right]=J=coul\cdot V=h\cdot Hz}
E
n
e
r
g
i
e
=
L
a
d
u
n
g
⋅
S
p
a
n
n
u
n
g
=
P
l
a
n
c
k
′
s
c
h
e
K
o
n
s
t
a
n
t
e
⋅
F
r
e
q
u
e
n
z
{\displaystyle Energie=Ladung\cdot Spannung=Planck'sche\,Konstante\cdot Frequenz}
Ein atomares System hat stationäre (nichtstrahlende) Zustände mit bestimmten diskreten Energiewerten. Elektronen können sich nur auf bestimmten (diskreten) Kreisbahnen um den Atomkern bewegen. Diese Kreisbahnen sind stabil, die Elektronen strahlen dabei keine Energie ab.Ein atomares System kann seine Energie nur ändern, indem es von einem stationären Zustand in einen anderen stationären Zustand übergeht. Wenn mit dem Übergang Emission oder Absorption von Strahlung verknüpft ist, so ist deren Frequenz mit der Energieänderung durch die Frequenzbedingung verbunden. Wobei Frequenzbedingung bedeutet, dass der Übergang von einer auf die nächste Bahn sprunghaft erfolgt. Jeder Quantensprung ist mit der Aufnahme oder Abgabe von Energie verbunden, die genau der Differenz der Energieniveaus entspricht.Die Elektronen können nur diskrete Bahnen annehmen. Der Drehimpuls dieser Bahnen entspricht sets einem ganzzahligen Vielfachen von
ℏ
{\displaystyle \hbar }
(
ℏ
=
h
2
π
)
{\displaystyle \left(\,\hbar ={h \over 2\pi }\,\right)}
Daraus folgt:
L
=
n
⋅
ℏ
[
L
]
=
1
⋅
J
⋅
s
e
c
{\displaystyle \mathrm {L=} n\cdot \hbar \qquad \left[\,L\,\right]=1\cdot J\cdot sec}
n
∈
N
ℏ
=
h
2
π
{\displaystyle n\in \mathbb {N} \qquad \hbar \mathrm {=} {h \over 2\pi }}
ℏ
{\displaystyle \hbar }
2
⋅
ℏ
{\displaystyle 2\cdot \hbar }
r
n
=
h
2
⋅
ϵ
0
m
e
⋅
e
2
⋅
π
⋅
n
2
[
r
n
]
=
m
=
(
J
⋅
s
e
c
)
2
⋅
A
s
e
c
V
m
k
g
⋅
c
o
u
l
2
⋅
1
⋅
1
2
{\displaystyle r_{n}={h^{2}\cdot \epsilon _{0} \over m_{e}\cdot e^{2}\cdot \pi }\cdot n^{2}\qquad \left[\,r_{n}\,\right]=m={(J\cdot sec)^{2}\cdot {Asec \over Vm} \over kg\cdot coul^{2}\cdot 1}\cdot 1^{2}}
R
a
d
i
u
s
=
(
P
l
a
n
c
k
′
s
c
h
e
K
o
n
s
t
.
)
2
⋅
ϵ
0
E
l
e
k
t
r
o
n
e
n
m
a
s
s
e
⋅
E
l
e
m
e
n
t
a
r
l
a
d
u
n
g
2
⋅
P
i
⋅
B
a
h
n
Z
a
h
l
{\displaystyle Radius={(Planck'scheKonst.)^{2}\cdot \epsilon _{0} \over Elektronenmasse\cdot Elementarladung^{2}\cdot Pi}\cdot BahnZahl}
W
n
=
−
1
8
⋅
m
e
⋅
e
4
ϵ
0
2
⋅
h
2
⋅
1
n
2
[
W
n
]
=
J
=
k
g
⋅
c
o
u
l
4
A
s
e
c
V
m
⋅
J
2
⋅
s
e
c
2
{\displaystyle W_{n}\ =\ -{1 \over 8}\cdot {m_{e}\cdot e^{4} \over \epsilon _{0}^{\;2}\,\cdot h^{2}}\cdot {\mathrm {1} \over n^{2}}\qquad \left[\,W_{n}\,\right]=J={kg\cdot coul^{4} \over {Asec \over Vm}\cdot J^{2}\cdot sec^{2}}}
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{\displaystyle m_{e}\mathrm {=e^{-}-masse} ;\;e\mathrm {=Elementarlad.} ;\;\epsilon _{0}{,}h\mathrm {=const.} ;\;n\in \mathbb {N} }
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{\displaystyle f\mathrm {=} {W_{m}\mathrm {-} W_{n} \over h}\mathrm {=} f_{R}\cdot \left({\mathrm {1} \over n^{2}}\mathrm {-} {\mathrm {1} \over m^{2}}\right)\qquad n,m\in \mathbb {N} }
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{\displaystyle f_{R}\mathrm {=} {m_{e}\cdot e^{4} \over \mathrm {8} \,\epsilon _{0}^{\;2}\,\cdot h^{3}}\mathrm {=3{,}29\cdot 10^{15}Hz} \qquad m_{e}\mathrm {=e^{-}-masse} ;\;e\mathrm {=Elementarlad.} ;\;\epsilon _{0}{,}h\mathrm {=const.} }
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{\displaystyle f_{K}\;\mathrm {=} \;(Z\mathrm {-1} )^{2}\cdot f_{R}\cdot \left({\mathrm {1} \over \mathrm {1^{2}} }\mathrm {-} {\mathrm {1} \over n^{2}}\right)\qquad Z\mathrm {=Ordnungszahl} ;\;n\mathrm {>1} ;\;n\in \mathbb {N} }
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{\displaystyle Z={z \over t}={Impulse \over Beobachtungszeit}}
absoluter:
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{\displaystyle {\sqrt {Z}}}
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{\displaystyle {1 \over {\sqrt {Z}}}}
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{\displaystyle \operatorname {N} (t)=N_{0}\cdot e^{-k\cdot t}\qquad k={\ln {1 \over 2} \over T_{1 \over 2}};T_{1 \over 2}=Halbwertszeit}
0 = Anzahl der Teilchen zum Zeitpunkt 0
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{\displaystyle \operatorname {A} (t)=k\cdot \operatorname {N} (t)=A_{0}\cdot e^{-k\cdot t}\qquad \left[\,\operatorname {A} (t)\,\right]=Bq={1 \over sec}}
Bei beiden Formeln muss man zunächst über bspw. die Angabe der Halbwertszeit die Konstante k berechnen. Zum Beispiel (hier mit Halbwertszeit!):
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{\displaystyle k={\ln 0{,}5 \over Halbwertszeit}}
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{\displaystyle D={\Delta W \over \Delta m}={Energie \over Masse}\quad \left[\,D\,\right]={J \over kg}=Gray}
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{\displaystyle H=Q\cdot D\quad \left[\,H\,\right]={J \over kg}=Sievert(Sv)\quad Q\approx {\begin{cases}1&\mathrm {fuer\,Roentgen-,\,\beta -,\,\gamma -Strahlung} \\10&\mathrm {fuer\,schnelle\,Neu-\,und\,Protonen} \\20&\mathrm {fuer\,\alpha -Strahlung} \end{cases}}}
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{\displaystyle \pi \approx 3{,}14159}
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{\displaystyle h=6{,}6260755\cdot 10^{-34}\,{\rm {{J\,s}=4{,}135671\cdot 10^{-15}e{\rm {Vs}}}}}
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{\displaystyle \hbar ={\frac {h}{2\pi }}=1{,}0545727\cdot 10^{-34}\,{\rm {J\,s}}}
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{\displaystyle \epsilon _{0}=8{,}85419\cdot 10^{-12}{\frac {A\cdot s}{V\cdot m}}}
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{\displaystyle \mu _{0}=1{,}25664\cdot 10^{-6}\cdot {T\cdot m \over A}}
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{\displaystyle 1eV=1e^{-}\cdot 1V=1{,}602\cdot 10^{-19}C\cdot 1V=1{,}602\cdot 10^{-19}J}
![{\displaystyle s=v\cdot t\qquad \left[\,s\,\right]=m={m \over s}\cdot s\qquad Strecke=Geschwindigkeit\cdot Zeit}](https://wikimedia.org/api/rest_v1/media/math/render/svg/69adb6093f0956e3a2abe4d9345a700837974579)
![{\displaystyle s={1 \over 2}\cdot a\cdot t^{2}\qquad \left[\,s\,\right]=m={m \over s^{2}}\cdot s^{2}\qquad Strecke={1 \over 2}\cdot Beschleunigung\cdot Zeit^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bfd5d511ec99e89db3d3b104da9842b228bf82ef)
![{\displaystyle v=a\cdot t\qquad \left[\,v\,\right]={m \over s}={m \over s^{2}}\cdot s\qquad Geschwindigkeit=Beschleungfigung\cdot Zeit}](https://wikimedia.org/api/rest_v1/media/math/render/svg/538aeed3da59354985589a6824f36e319fad125e)
![{\displaystyle F=m\cdot a\qquad \left[\,F\,\right]=N=kg\cdot {m \over s^{2}}\qquad Kraft=Masse\cdot Beschleunigung}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c2706ebfb7007b3241b76be544d588d3fa2e41a8)
![{\displaystyle E_{Pot}=m\cdot g\cdot h\quad \left[\,E_{Pot}\,\right]=J=kg\cdot {m \over s^{2}}\cdot m\quad Energie=Masse\cdot Erdbeschl.\cdot Hoehe}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56a9178be434475c7385b583118d7c7dae91f717)
![{\displaystyle E_{Kin}={1 \over 2}\cdot m\cdot v^{2}\quad \left[\,E_{Kin}\,\right]=J=kg\cdot \left({m \over s}\right)^{2}\quad Energie={1 \over 2}\cdot Masse\cdot Geschw.^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d99917e36925334142a4c5250af6ab4268616836)
![{\displaystyle E_{Spann}={1 \over 2}\cdot D\cdot s^{2}\quad \left[\,E_{Spann}\,\right]=J={N \over m}\cdot m^{2}\quad En.={1 \over 2}\cdot Federkonst.\cdot Strecke^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ad4e0edb84761fc8e02544b283c5f2d6fecaaad7)
![{\displaystyle D={F \over s}\quad \left[\,D\,\right]={N \over m}={{kg\cdot m \over sec^{2}} \over m}\quad Federkonstante={Kraft \over Srecke}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/97740795681a701fad3101d379875fd78460185b)
![{\displaystyle {\overrightarrow {p}}=m\cdot {\overrightarrow {v}}\qquad \left[\,p\,\right]=kg\cdot {m \over s}\qquad Impuls=Masse\cdot Geschwindigkeit}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed1b797faff4ee8d207508e002ef9174196ff01)
![{\displaystyle F_{Z}=m\cdot r\cdot \omega ^{2}={m\cdot v^{2} \over r}\quad \left[\,F_{Z}\,\right]=N={kg\cdot \left({m \over s}\right)^{2} \over m}\quad Kraft={Masse\cdot Geschw.^{2} \over Radius}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0f87dbe04274e4043358f86a4d485e1b27a5aa0)
![{\displaystyle \omega =2\pi \cdot f={2\pi \over T}\quad \left[\,\omega \,\right]={1 \over s}\quad Winkelgeschw.=2\pi \cdot Uml.Frequenz={2\pi \over Umlaufzeit}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1e8c1546cc5443f02b774881d8cf9492f66ff464)
![{\displaystyle L=r\cdot p_{\bot }\qquad \left[\,L\,\right]=m\cdot {kg\cdot m \over sec}=J\cdot sec\qquad Drehimpuls=Radius\cdot Senkr.Impuls}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d14bb0762a4a8ac8caef6c05a859d93499be3969)
![{\displaystyle L=r\cdot m\cdot v\qquad \left[\,L\,\right]=m\cdot kg\cdot {m \over sec}=Nm\cdot sec=J\cdot sec}](https://wikimedia.org/api/rest_v1/media/math/render/svg/04a664ef197296239cc0b5246767241d89ea2b1c)
![{\displaystyle I_{=}={Q \over t}\qquad \left[\,I_{=}\,\right]={Coul \over sec}\qquad Strom={Ladung \over Zeit}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/84bcb896edcaf98b12c6c5b883c0a682909730b8)
![{\displaystyle I_{\approx }={\dot {Q}}={dq \over dt}\qquad \left[\,I_{\approx }\,\right]={Coul \over sec}\qquad Strom={Ladungsdiff. \over Zeitdiff.}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a62638df53ea08143c2bd4ed9ebf3f95ec62afbe)
![{\displaystyle U={W \over q}\qquad \left[\,U\,\right]=V={J \over Coul}={N\cdot m \over Coul}\qquad Spannung={Arbeit \over Ladung}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/17e9f631868d116055f7734294e2a39931b2502b)
![{\displaystyle R={U \over I}\qquad \left[\,R\,\right]=\Omega ={V \over A}\qquad Widerstand={Spannung \over Strom}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8c42a4cc073798a6cbe1542b776801936c00a8b2)
![{\displaystyle P=U\cdot I\qquad \left[\,P\,\right]=W=V\cdot A={J \over s}={N\cdot m \over s}\qquad Leistung=Spannung\cdot Strom}](https://wikimedia.org/api/rest_v1/media/math/render/svg/212d1aece99ddeaca2a1de0f21a635e84e0e6d68)
![{\displaystyle {\begin{matrix}W&=&P\cdot t&&[\,W\,]=J=Watt\cdot sec&&Arbeit&=&Leistung\cdot Zeit\\\ &=&U\cdot I\cdot t&&[\,W\,]=J=V\cdot A\cdot sec\ &&\ &=&Strom\cdot Spannung\cdot Zeit\end{matrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/49048032f8eaa54666460fe1f1305d1275dc68db)
![{\displaystyle {\overrightarrow {E}}={{\overrightarrow {F_{e}}} \over Q}\qquad \left[\,{\overrightarrow {E}}\,\right]=\,{N \over Coul}\qquad Elektr.Feld={Kraft \over Ladung}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f3b4da8b061811a7850786ea0b049087c26a9d47)
![{\displaystyle F_{Coul}={1 \over 4\pi \epsilon _{0}\epsilon _{r}}\cdot {Q\!\cdot \!q \over r^{2}}\quad \left[\,F_{Coul}\,\right]=N={1 \over {Far \over m}}\cdot {Coul\cdot Coul \over m^{2}}\quad Kraft=const.\cdot {Lad_{1}\cdot Lad_{2} \over Abstand^{2}.}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/113081bdef16b12021ab349928c8f81ef9799231)
![{\displaystyle E={U \over d}\qquad \left[\,E\,\right]={N \over coul}={V \over m}\qquad Elektr.Feld={Spannung \over Plattenabst.}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/239f5d9974e5dcd6ed0d93e56474ee4c87a341b1)
![{\displaystyle F_{Feld}=q\cdot {\overrightarrow {E}}=q\cdot {U \over d}\quad \left[F_{Feld}\right]=N=Coul\cdot {N \over Coul}=Coul\cdot {V \over m}\quad Kraft=Ladung\cdot {Spannung \over Plattenabst.}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fb8227bad7b49d95f8941fbcc7a8de3c9bda5711)
![{\displaystyle \sigma ={Q \over A}\qquad \left[\,\sigma \,\right]={Coul \over m^{2}}\qquad Sigma={Ladung \over Flaeche}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5cfae0ff9153712974f052020f8e6159c1160ed9)
![{\displaystyle C={Q \over U}\qquad \left[\,C\,\right]=Far={Coul \over V}\qquad Kapazitaet={Ladung \over Spannung}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e544914a6fa7ebe46808bb2ff9e28a17171d788e)
![{\displaystyle C=\epsilon _{r}\cdot \epsilon _{0}\cdot {A \over d}\qquad \left[\,C\,\right]=Far=1\cdot {Asec \over Vm}\cdot {m^{2} \over m}\qquad Kapazitaet=\epsilon _{r}\cdot \epsilon _{0}\cdot {Flaeche \over Abstand}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/832d97419c83bb60bded11860bd91231ae8ccefa)
![{\displaystyle E_{Kon}={1 \over 2}\cdot C\cdot U^{2}\quad \left[\,E_{Kon}\,\right]=J=Far\cdot V^{2}\quad Energie={1 \over 2}\cdot Kapazitaet\cdot Spannung^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7bad518d3b939e333b070865474f9d2659c6942b)
![{\displaystyle U_{Ind}=-n\cdot {\dot {\Phi }}\qquad \left[\,U_{Ind}\,\right]=V\qquad Indunktion=-Windugszahl\cdot {\dot {\Phi }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6bf0a9e69d09cd09e2de010a717f48ab9a6b6e4d)
![{\displaystyle \Phi =A\cdot B\qquad \left[\,\Phi \,\right]=m^{2}\cdot T\qquad Spulenquerschnittsflaeche\cdot Magnetfeld}](https://wikimedia.org/api/rest_v1/media/math/render/svg/50c9678bba45f1d5a25d7d407791df41f480a8d3)
![{\displaystyle {\dot {\Phi }}={\dot {A}}\cdot B+A\cdot {\dot {B}}\qquad \qquad \qquad \left[\,{\dot {\Phi }}\,\right]={m^{2}\cdot T \over sec}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bfff62f172a999a1ae4ec7d0c0a7cf642595bbc3)
![{\displaystyle U_{Ind_{Selbst}}=-L\cdot {\dot {I}}\quad \left[\,U\,\right]=V=Henry\cdot {A \over sec}\quad Sp.=-Indukt.\cdot Stromaenderung}](https://wikimedia.org/api/rest_v1/media/math/render/svg/46945e3bda360a0a4f0a88e5add7b2abe823917e)
![{\displaystyle L={\frac {\mu _{0}\cdot \mu _{r}\cdot A\cdot n^{2}}{l}}\qquad \left[\,L\,\right]=Henry={V\cdot sec \over A}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6f0f056809e22cb2a989368268c99192b7833322)
![{\displaystyle B_{Spule}=\mu _{0}\cdot \mu _{r}\cdot {n\cdot I \over l}\qquad \left[\,B_{Sp}\,\right]=T={N \over Am}\qquad Flussd.=\mu _{0}\cdot \mu _{r}\cdot {Wind.zahl\cdot Strom \over Spulenlaenge}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6f992111737ca1c33270e941b764b35922159b28)
![{\displaystyle E_{Spule}={1 \over 2}\cdot L\cdot I^{2}\qquad \left[\,E_{Spule}\,\right]=J=Henry\cdot A^{2}\qquad Energie={1 \over 2}\cdot SelbstInd.\cdot Strom^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4fa50c78fb7664196d5d6d821f62295b57436ff5)
![{\displaystyle {\overrightarrow {B}}={{\overrightarrow {F_{m}}} \over I\cdot {\overrightarrow {l_{\bot }}}}\qquad \left[\,B\,\right]=T={N \over A\cdot m}\qquad Flussdichte={Magn.Kraft \over Strom\cdot Laenge}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ab5cbf7516ce1350c925b3c356ef52e1337f3a5)
![{\displaystyle F_{L}=Q\cdot v\cdot B_{\bot }\quad \left[\,F_{L}\,\right]=N=coul\cdot {m \over sec}\cdot T\quad Kraft=Lad.\cdot Geschw.\cdot Senkr.M\!-\!Feld}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9196b83101220ffe8603e6265cbd3daf6891310e)
![{\displaystyle U_{H}=d\cdot v\cdot B_{\bot }\quad \left[\,U_{H}\,\right]=V=m\cdot {m \over sec}\cdot T\quad Sp.=Plaettch.breite\cdot Geschw.\cdot Senkr.M\!-\!Feld}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8c81967ddc60922c95a72f2f3617e254759b3973)
![{\displaystyle {\hat {U}}=n\cdot B\cdot A\cdot \omega \qquad \left[\,U\,\right]=V=1\cdot T\cdot m^{2}\cdot {1 \over sec}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/23e2454765e4900b05d360e9fc615c7aa4a74bef)
![{\displaystyle R_{C}={1 \over \omega \cdot C}\qquad \left[\,R_{C}\,\right]=\Omega \qquad Widerstand=\omega \cdot {1 \over Winkelgeschw.\cdot Kapazitaet}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e719c12e5dfbe65ba010bec9dfe8c13199d393db)
![{\displaystyle R_{L}=\omega \cdot L\qquad \left[\,R_{L}\,\right]=\Omega \qquad Widerstand=Winkelgeschw.\cdot Selbstind.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/12443be4a789e5d6e4e2bc343b93cea3dedf5be9)
![{\displaystyle \omega =2\pi \cdot f={2\pi \over T}\qquad \left[\,\omega \,\right]={1 \over s}\qquad Winkelgeschw.=2\pi \cdot Uml.Frequenz={2\pi \over Umlaufzeit}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d67d747d1a52647ecda85178c2d8c55584dd559f)
![{\displaystyle P_{wirk}=U_{eff}\cdot I_{eff}\cdot \cos(\alpha )\qquad \left[\,P_{wirk}\,\right]=V\cdot A={J \over s}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/08e335172441c4273319af3a26e81fd8158148fe)
![{\displaystyle F_{Rueck}=-D\cdot s\qquad \left[\,F_{Rueck}\,\right]=N={N \over m}\cdot m\qquad Kraft=-Federkonstante\cdot Strecke}](https://wikimedia.org/api/rest_v1/media/math/render/svg/afceec241c112f00953fd158bca1a50267de350b)
![{\displaystyle c=\lambda \cdot f\qquad \left[\,c\,\right]={m \over sec}=m\cdot {1 \over sec}\qquad Geschw.=Wellenl.\cdot Frequenz}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b0fcf3870b95692e6275a432c499a543be14027a)
![{\displaystyle \operatorname {s_{hin}} \,(t,\,x)={\hat {s}}\cdot \sin \,\left[\,2\cdot \pi \cdot \left(\,{t \over T}-{x \over \lambda }\,\right)\,\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6bd14a1691f23411f2ae46ebfa04707c4ad05c24)
![{\displaystyle \operatorname {s_{rueck_{lose}}} \,(t,\,x)=\mathbf {+} {\hat {s}}\cdot \sin \,\left[\,2\cdot \pi \cdot \left(\,{t \over T}\mathbf {+} {x \over \lambda }\,\right)\,\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a6cb63736f1324b3b655304c5752f60af61a6c44)
![{\displaystyle \operatorname {s_{rueck_{fest}}} \,(t,\,x)={\mathit {\mathbf {-} }}{\hat {s}}\cdot \sin \,\left[\,2\cdot \pi \cdot \left(\,{t \over T}\mathbf {+} {x \over \lambda }\,\right)\,\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3403ab52151c2db33603bca53c3fb4dd4b15a902)
![{\displaystyle W_{phot}=h\cdot f\qquad \left[\,W_{Phot}\,\right]=J=J\cdot s\cdot Hz=J\cdot s\cdot {1 \over s}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d6f938ef3a5dd3bbd9e2de1229b901df96e44ce5)
![{\displaystyle W_{e^{-}}=W_{phot}=e\cdot U=h\cdot f_{max}\quad \left[\,W_{e^{-}}\,\right]=J=coul\cdot V=h\cdot Hz}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a96812c59e8264f379526af1423e641e0573483c)
![{\displaystyle \mathrm {L=} n\cdot \hbar \qquad \left[\,L\,\right]=1\cdot J\cdot sec}](https://wikimedia.org/api/rest_v1/media/math/render/svg/36b440a9e0a137a4faec45baae336c5c61a64652)
![{\displaystyle r_{n}={h^{2}\cdot \epsilon _{0} \over m_{e}\cdot e^{2}\cdot \pi }\cdot n^{2}\qquad \left[\,r_{n}\,\right]=m={(J\cdot sec)^{2}\cdot {Asec \over Vm} \over kg\cdot coul^{2}\cdot 1}\cdot 1^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8a618cf82da6d3161d849fc5463582ae88295ca4)
![{\displaystyle W_{n}\ =\ -{1 \over 8}\cdot {m_{e}\cdot e^{4} \over \epsilon _{0}^{\;2}\,\cdot h^{2}}\cdot {\mathrm {1} \over n^{2}}\qquad \left[\,W_{n}\,\right]=J={kg\cdot coul^{4} \over {Asec \over Vm}\cdot J^{2}\cdot sec^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d88fbe1af21aad945e410807e72b2fa1dabd86f)
![{\displaystyle \operatorname {A} (t)=k\cdot \operatorname {N} (t)=A_{0}\cdot e^{-k\cdot t}\qquad \left[\,\operatorname {A} (t)\,\right]=Bq={1 \over sec}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bbcaf7343c00afe71cffae46274bf4e23aa3c8ee)
![{\displaystyle D={\Delta W \over \Delta m}={Energie \over Masse}\quad \left[\,D\,\right]={J \over kg}=Gray}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2336282cf34f8ec08d75de7cac9729785760b5df)
![{\displaystyle H=Q\cdot D\quad \left[\,H\,\right]={J \over kg}=Sievert(Sv)\quad Q\approx {\begin{cases}1&\mathrm {fuer\,Roentgen-,\,\beta -,\,\gamma -Strahlung} \\10&\mathrm {fuer\,schnelle\,Neu-\,und\,Protonen} \\20&\mathrm {fuer\,\alpha -Strahlung} \end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/220f7969121cbc01c2464eccc54e1a07780e8a1b)
