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For more info see http://www.lyx.org/ \lyxformat 544 \begin_document \begin_header \save_transient_properties true \origin unavailable \textclass article \use_default_options true \maintain_unincluded_children false \language english \language_package default \inputencoding auto \fontencoding global \font_roman "default" "default" \font_sans "default" "default" \font_typewriter "default" "default" \font_math "auto" "auto" \font_default_family default \use_non_tex_fonts false \font_sc false \font_osf false \font_sf_scale 100 100 \font_tt_scale 100 100 \use_microtype false \use_dash_ligatures true \graphics default \default_output_format default \output_sync 0 \bibtex_command default \index_command default \paperfontsize default \use_hyperref false \papersize default \use_geometry false \use_package amsmath 1 \use_package amssymb 1 \use_package cancel 1 \use_package esint 1 \use_package mathdots 1 \use_package mathtools 1 \use_package mhchem 1 \use_package stackrel 1 \use_package stmaryrd 1 \use_package undertilde 1 \cite_engine basic \cite_engine_type default \use_bibtopic false \use_indices false \paperorientation portrait \suppress_date false \justification true \use_refstyle 1 \use_minted 0 \index Index \shortcut idx \color #008000 \end_index \secnumdepth 3 \tocdepth 3 \paragraph_separation indent \paragraph_indentation default \is_math_indent 0 \math_numbering_side default \quotes_style english \dynamic_quotes 0 \papercolumns 1 \papersides 1 \paperpagestyle default \tracking_changes false \output_changes false \html_math_output 0 \html_css_as_file 0 \html_be_strict false \end_header \begin_body \begin_layout Standard 1. Formelumstellungen \end_layout \begin_layout Standard In Technik, Physik und Mathematik sind gegenseitige Beziehungen zwischen Größen als Formeln bekannt. Es handelt sich um Gleichungen, die entweder Identitäten sind (für alle Belegungen der Variablen gelten) oder innerhalb eines bestimmten Definitionsber eiches die objektive Realität widerspiegeln. Häufig sind solche Beziehungen ihrër mathematischen Struktur nach gleichartig aufgebaut. Die Bearbeitung der völlig: verschiedenen Gebieten entnommenen Gesetzmäßigkeite n erfolgt deshalb oft analog. Ein und derselbe Typ einer mathematischen Beziehung beschreibt und charakterisi ert also dann physikalische oder technische Verhältnisse aus verschiedenen Sachgebieten. \end_layout \begin_layout Standard Beispiele: \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Typ: \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $\boldsymbol{A}=\boldsymbol{B}\cdot\boldsymbol{C}$ \end_inset \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $s=v\cdot t$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout gleichförmige \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Bewegung \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $\sin\alpha=n\sin\beta$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Brechungs- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout gesetz Optik \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $U=R\cdot I$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout OHmsches \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Gesetz \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $\Phi=I\cdot\omega$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Lichtstrom \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $v=r\cdot\omega$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Dreh- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout bewegung \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $RT=p\cdot V$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Gas- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout gleichung \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $F_{\mathrm{R}}=\mu\cdot F_{\mathrm{N}}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Reibung \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $u=\pi\cdot d$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Kreisumfang \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Typ: \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $\boldsymbol{A}=\boldsymbol{B}\cdot\boldsymbol{C}^{2}$ \end_inset \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $a_{\mathrm{r}}=\omega\cdot r^{2}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Radial- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout beschleunigung \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $E=m\cdot c^{2}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Gleichung von \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout EINSTEIN \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $J=\frac{\varrho}{2}cu^{2}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Schallstärke \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $s=\frac{g}{2}\cdot t^{2}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Freier Fall \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $F_{z}=\frac{m}{r}\cdot v^{2}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Zentri- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout fugalkraft \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $A=\pi\cdot r^{2}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Kreisfläche \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $P=R\cdot I^{2}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Elektrische \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Leistung \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $A_{1}=A_{0}\cdot k^{2}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Ähnlichkeit \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout bei Flächen \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $T=2\pi\cdot\sqrt{\frac{l}{g}}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $T=2\pi\cdot\sqrt{\frac{m}{D}}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $c=\sqrt{\frac{E}{\varrho}}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $d=a\cdot\sqrt{2}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $\boldsymbol{A}=\boldsymbol{B}\cdot\sqrt{\boldsymbol{C}}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Periodendauer \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout beim Faden- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout pendel \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Periodendauer \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout physikalisches \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Pendel \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Schall- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout geschwindig- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout keit \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Quadrat- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout diagonale \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Typ: \end_layout \end_inset \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 \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \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 \begin_inset Text \begin_layout Plain Layout Dichte- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout bestimmung \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \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 \begin_inset Text \begin_layout Plain Layout KiRchHoFF- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout sches Gesetz \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $f=\frac{a\cdot b}{a+b}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Brennweite \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout beim Spiegel \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \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 \begin_inset Text \begin_layout Plain Layout Betrag des Wider- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout standsoperators \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Parallelschaltung \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Typ: \end_layout \end_inset \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 \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \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 \begin_inset Text \begin_layout Plain Layout Anziehung \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout von Massen \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \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 \begin_inset Text \begin_layout Plain Layout CoulomB- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Gesetz \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \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 \begin_inset Text \begin_layout Plain Layout Magnetisches \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Feld \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $E=\frac{I\cdot\cos\varepsilon}{r^{2}}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Beleuchtungs- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout stärke \begin_inset Formula $\quad$ \end_inset . \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $\mathrm{Typ}:$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $\boldsymbol{A}=\boldsymbol{B}(\mathbf{1}+\boldsymbol{C})$ \end_inset \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $l=$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $l_{0}(1+\alpha\Delta t)$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Längen- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout ausdehnung \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $V=$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $V_{0}(1+\gamma\Delta t)$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Volumen- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout ausdehnung \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $R=$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $R_{0}(1+\alpha t)$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Widerstand \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout in Abhängig- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout keit von der \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Temperatur \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $a_{n}-a_{1}=$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $d(n-1)$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout arithmetische \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Folge \end_layout \end_inset \end_inset \end_layout \end_inset \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 \begin_inset Text \begin_layout Plain Layout Schritt \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Prinzip \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Muster \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout t \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Aufgabenstellung \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout (sachgebietsbezogen) \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout In einer Batterieschaltung sind \begin_inset Formula $n$ \end_inset Ele- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout mente in Reihe (hintereinander) ge- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout schaltet. Jedes Element hat die Span- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout nung \begin_inset Formula $U$ \end_inset und den inneren Widerstand \end_layout \end_inset \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 \begin_inset Text \begin_layout Plain Layout Außenwiderstand \begin_inset Formula $R_{\mathrm{a}}$ \end_inset ist gesucht. \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Aufstellen der Formel \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout (bekannt oder gegeben, evtl. aus \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout der Formelsammlung zu entnehmen) \end_layout \end_inset \end_inset \end_layout \end_inset \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 \begin_inset Text \begin_layout Plain Layout \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Formulierung der mathema- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout tischen Aufgabe \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout (Kennzeichnung der gesuchten \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Größe) \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \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 \begin_inset Text \begin_layout Plain Layout ist nach \begin_inset Formula $R_{\mathrm{a}}$ \end_inset aufzulösen. \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout t \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Beschreibung der mathematischen \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Terme \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout (Lösungsplan) \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Die gesuchte Variable steht als Sum- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout mand im Nenner eines Bruches. \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Elementare 0perationen zur Verein- \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout fachung \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout (falls erforderlich, Wurzeln oder \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Brüche beseitigen - falls unbek. \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Variable innerhalb eines durch \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Klammern eingeschlossenen Terms, \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Auflösen desselben oft zweckmäßig) \end_layout \end_inset \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Tabular \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 \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 \end_inset \end_layout \end_inset \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 \begin_inset Text \begin_layout Plain Layout D Bessere Gestaltung der gefundenen \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Formel \end_layout \end_inset \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