2855 lines
48 KiB
Plaintext
2855 lines
48 KiB
Plaintext
#LyX 2.3 created this file. For more info see http://www.lyx.org/
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1.
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Formelumstellungen
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\end_layout
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\begin_layout Standard
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In Technik, Physik und Mathematik sind gegenseitige Beziehungen zwischen
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Größen als Formeln bekannt.
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Es handelt sich um Gleichungen, die entweder Identitäten sind (für alle
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Belegungen der Variablen gelten) oder innerhalb eines bestimmten Definitionsber
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eiches die objektive Realität widerspiegeln.
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Häufig sind solche Beziehungen ihrër mathematischen Struktur nach gleichartig
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aufgebaut.
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Die Bearbeitung der völlig: verschiedenen Gebieten entnommenen Gesetzmäßigkeite
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n erfolgt deshalb oft analog.
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Ein und derselbe Typ einer mathematischen Beziehung beschreibt und charakterisi
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ert also dann physikalische oder technische Verhältnisse aus verschiedenen
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Sachgebieten.
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Beispiele:
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gleichförmige
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Bewegung
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gesetz Optik
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OHmsches
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Gesetz
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Lichtstrom
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Dreh-
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bewegung
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Gas-
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gleichung
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Reibung
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Typ:
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<cell alignment="left" valignment="top" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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\begin_inset Formula $\boldsymbol{A}=\boldsymbol{B}\cdot\boldsymbol{C}^{2}$
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\end_inset
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\end_layout
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\begin_inset Text
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\begin_layout Plain Layout
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\begin_inset Formula $a_{\mathrm{r}}=\omega\cdot r^{2}$
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\end_layout
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\end_inset
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Radial-
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\begin_inset Text
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beschleunigung
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\begin_inset Formula $E=m\cdot c^{2}$
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\end_layout
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\begin_inset Text
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\begin_layout Plain Layout
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Gleichung von
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EINSTEIN
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|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $J=\frac{\varrho}{2}cu^{2}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Schallstärke
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="2" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $s=\frac{g}{2}\cdot t^{2}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Freier Fall
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="3" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $F_{z}=\frac{m}{r}\cdot v^{2}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Zentri-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
fugalkraft
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="2" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $A=\pi\cdot r^{2}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Kreisfläche
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="3" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $P=R\cdot I^{2}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Elektrische
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Leistung
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="3" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $A_{1}=A_{0}\cdot k^{2}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Ähnlichkeit
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
bei Flächen
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $T=2\pi\cdot\sqrt{\frac{l}{g}}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $T=2\pi\cdot\sqrt{\frac{m}{D}}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $c=\sqrt{\frac{E}{\varrho}}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $d=a\cdot\sqrt{2}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $\boldsymbol{A}=\boldsymbol{B}\cdot\sqrt{\boldsymbol{C}}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="3" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Periodendauer
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
beim Faden-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
pendel
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="3" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Periodendauer
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
physikalisches
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Pendel
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="3" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Schall-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
geschwindig-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
keit
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="2" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Quadrat-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
diagonale
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="2" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Typ:
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $\boldsymbol{A}=\frac{\boldsymbol{B}\cdot\boldsymbol{C}}{\boldsymbol{D}\pm\boldsymbol{E}}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="3" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $\varrho=\frac{\gamma_{\mathrm{F}}\cdot G}{G-G_{\mathrm{F}}}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Dichte-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
bestimmung
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="3" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $R=\frac{R_{1}\cdot R_{2}}{R_{1}+R_{2}}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
KiRchHoFF-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
sches Gesetz
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="3" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $f=\frac{a\cdot b}{a+b}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Brennweite
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
beim Spiegel
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="4" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $Z=\frac{\omega L_{1}\cdot L_{2}}{L_{1}+L_{2}}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Betrag des Wider-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
standsoperators
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Parallelschaltung
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="2" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Typ:
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $\boldsymbol{A}=\boldsymbol{B}\frac{\boldsymbol{C}\cdot\boldsymbol{D}}{\boldsymbol{E}^{2}}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="3" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $F=\gamma\frac{m_{1}\cdot m_{2}}{r^{2}}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Anziehung
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
von Massen
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="3" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $F=\frac{1}{4\pi\varepsilon}\frac{Q_{1}\cdot Q_{2}}{s^{2}}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
CoulomB-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Gesetz
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="3" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $F=c\frac{m_{1}\cdot m_{2}}{e^{2}}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Magnetisches
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Feld
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="3" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $E=\frac{I\cdot\cos\varepsilon}{r^{2}}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Beleuchtungs-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
stärke
|
|
\begin_inset Formula $\quad$
|
|
\end_inset
|
|
|
|
.
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="2" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $\mathrm{Typ}:$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $\boldsymbol{A}=\boldsymbol{B}(\mathbf{1}+\boldsymbol{C})$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="4" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $l=$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $l_{0}(1+\alpha\Delta t)$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Längen-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
ausdehnung
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="4" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $V=$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $V_{0}(1+\gamma\Delta t)$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Volumen-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
ausdehnung
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="6" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $R=$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $R_{0}(1+\alpha t)$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Widerstand
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
in Abhängig-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
keit von der
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Temperatur
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="4" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $a_{n}-a_{1}=$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $d(n-1)$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
arithmetische
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Folge
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Die Beziehungen (Gleichungen, Formeln) enthalten in den Termen Variablen,
|
|
die voneinander abhängen.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Die Beziehung
|
|
\begin_inset Formula $s\quad v\quad.\quad t$
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Formula $($
|
|
\end_inset
|
|
|
|
Weg = Geschwindigkeit
|
|
\begin_inset Formula $\cdot$
|
|
\end_inset
|
|
|
|
Zeit
|
|
\begin_inset Formula $)$
|
|
\end_inset
|
|
|
|
kann als Funktionsgleichung
|
|
\begin_inset Formula
|
|
\[
|
|
s(t)\quad=\quad v\cdot t\quad[s\text{ und }t\text{ variabel, }v\text{ konstant }]
|
|
\]
|
|
|
|
\end_inset
|
|
|
|
dargestellt werden.
|
|
Bedeutung: Der zurückgelegte Weg
|
|
\begin_inset Formula $s$
|
|
\end_inset
|
|
|
|
ist bei gleichförmig geradliniger Bewegung von der Zeit
|
|
\begin_inset Formula $t$
|
|
\end_inset
|
|
|
|
abhängig.
|
|
Entsprechend kann man schreiben:
|
|
\begin_inset Formula $U(R)=I\cdot R$
|
|
\end_inset
|
|
|
|
und
|
|
\begin_inset Formula $v(r)=\omega\cdot r$
|
|
\end_inset
|
|
|
|
und
|
|
\begin_inset Formula $F_{R}\left(F_{\mathrm{N}}\right)=\mu\cdot F_{\mathrm{N}}$
|
|
\end_inset
|
|
|
|
und
|
|
\begin_inset Formula $u(d)=\pi\cdot d$
|
|
\end_inset
|
|
|
|
usw.
|
|
Der Typ oiner solchen Abhängigkeit wird mathematisch durch die verallgemeinernd
|
|
e Symbolik
|
|
\begin_inset Formula $f(x)=\ldots$
|
|
\end_inset
|
|
|
|
beschrieben.
|
|
In der Regel ist in einer Formel eine bestimmte Variable gesucht (unbekannt),
|
|
die anderen Größen sind gegeben.
|
|
Nicht immer ist jedoch die unbekannte Variable in Abhängigkeit von den
|
|
anderen explizit dargestellt.
|
|
Dann muß die Formel erst nach einer bestimmten (umbekannten) Variablen
|
|
aufgelöst werden.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Das geschieht in folgender Weise:
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="6" columns="3">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Schritt
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Prinzip
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Muster
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell multirow="3" alignment="none" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
t
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="2" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Aufgabenstellung
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
(sachgebietsbezogen)
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="6" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
In einer Batterieschaltung sind
|
|
\begin_inset Formula $n$
|
|
\end_inset
|
|
|
|
Ele-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
mente in Reihe (hintereinander) ge-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
schaltet.
|
|
Jedes Element hat die Span-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
nung
|
|
\begin_inset Formula $U$
|
|
\end_inset
|
|
|
|
und den inneren Widerstand
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $R_{1}$
|
|
\end_inset
|
|
|
|
.
|
|
Die Gesamtstromstärke ist
|
|
\begin_inset Formula $I$
|
|
\end_inset
|
|
|
|
.
|
|
Der
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Außenwiderstand
|
|
\begin_inset Formula $R_{\mathrm{a}}$
|
|
\end_inset
|
|
|
|
ist gesucht.
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="3" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Aufstellen der Formel
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
(bekannt oder gegeben, evtl.
|
|
aus
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
der Formelsammlung zu entnehmen)
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $I=\frac{n\cdot U}{n\cdot R_{\mathrm{i}}+R_{\mathrm{a}}}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="4" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Formulierung der mathema-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
tischen Aufgabe
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
(Kennzeichnung der gesuchten
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Größe)
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="2" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $I=\frac{n\cdot U}{n\cdot R_{\mathrm{i}}+\boldsymbol{R}_{\mathrm{a}}}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
ist nach
|
|
\begin_inset Formula $R_{\mathrm{a}}$
|
|
\end_inset
|
|
|
|
aufzulösen.
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell multirow="3" alignment="none" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
t
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="3" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Beschreibung der mathematischen
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Terme
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
(Lösungsplan)
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="2" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Die gesuchte Variable steht als Sum-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
mand im Nenner eines Bruches.
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="7" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Elementare 0perationen zur Verein-
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
fachung
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
(falls erforderlich, Wurzeln oder
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Brüche beseitigen - falls unbek.
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Variable innerhalb eines durch
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Klammern eingeschlossenen Terms,
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Auflösen desselben oft zweckmäßig)
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="2" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $I\left(n\cdot R_{\mathrm{i}}+R_{\mathrm{a}}\right)=n\cdot U$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Formula $I\cdot n\cdot R_{\mathrm{i}}+I\cdot R_{\mathrm{a}}=n\cdot U$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
C Isolieren der unbekannten Variablen
|
|
\begin_inset Formula $I\cdot R_{\mathrm{a}}=n\cdot U-I\cdot n\cdot R_{1}$
|
|
\end_inset
|
|
|
|
(Ziel: Terme mit der unbekannten Variablen stehen isoliert auf einer Seite
|
|
der Beziehung) Division der gesamten Gleichung durch den Koeffizienten
|
|
(Beiwert)
|
|
\begin_inset Formula $R_{\mathrm{a}}=\frac{n\cdot U-I\cdot n\cdot R_{\mathrm{i}}}{I}$
|
|
\end_inset
|
|
|
|
der unbekannten Variablen (Zuvor ist gegebenenfalls die unbekannte Variable
|
|
auszuheben / auszuklammern)
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="2" columns="1">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="left" valignment="top">
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
D Bessere Gestaltung der gefundenen
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="left" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Formel
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Formula $R_{\mathrm{a}}=n\frac{U}{I}-nR_{1}$
|
|
\end_inset
|
|
|
|
oder:
|
|
\begin_inset Formula
|
|
\[
|
|
R_{\mathrm{a}}=n\left(\frac{U}{I}-R_{\mathrm{l}}\right)
|
|
\]
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Deutung und Diskussion Der Außenwiderstand kann bestimmt werden durch die
|
|
mit der Anzahl der Elemente multiplizierten Differenz von Gesamtwiderstand
|
|
und Innenwiderstand.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Beachten Sie: Bei der Umstellung von Formeln gelten die Gesetzmäßigkeiten
|
|
des Lösens von Gleichungen.
|
|
Es dürfen also nur äquivalente Umformungen vorgenommen werden.
|
|
Grundsätzlich darf auf beiden Seiten einer Gleichheitsbeziehung nur die
|
|
gleiche Operation ausgeführt werden, und zwar: Addition oder Subtraktion
|
|
eines Terms,.
|
|
Multiplikation mit einem von Null verschiedenen Term, Division durch einen
|
|
von Null verschiedenen Term, Potenzieren mit ungeradzahligem Exponenten,
|
|
Radizieren, sofern auf beiden Seiten positive Größen stehen.
|
|
Eine Division durch 0 oder durch einen Term, der den Wert 0 annehmen kann,
|
|
ist nicht zulässig.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
|
|
\end_layout
|
|
|
|
\end_body
|
|
\end_document
|