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exam_infos:preparation [2023/02/02 10:53] – [Do physics right] mexleadminexam_infos:preparation [2023/02/02 13:28] (aktuell) – [Do math right] mexleadmin
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 ===== Do math right ===== ===== Do math right =====
  
-  * calculate fractions in fractions correct: \begin{align*} {{{A}\over{B}}\over{C}} \quad &\neq \quad {{A}\over{{B}\over{C}}} \\ {{{A}\over{B}}\over{C}} = {{A}\over{{B}\cdot{C}}} \quad &\neq \quad {{A}\over{{B}\over{C}}} = {{A\cdot C}\over{B}} \end{align*}+  * calculate fractions in fractions (complex fractions) correct 
 +    * Be aware which is the longest fraction line: \\  \begin{align*} {{{A}\over{B}}\over{C}} \quad &\neq \quad {{A}\over{{B}\over{C}}} \\ {{{A}\over{B}}\over{C}} = {{A}\over{{B}\cdot{C}}} \quad &\neq \quad {{A}\over{{B}\over{C}}} = {{A\cdot C}\over{B}} \end{align*} 
 +    * Be aware how to reduce complex fractions by multiplying numerator and denominator with a factor: \\ \begin{align*} { { {{5 \cdot {{1}\over{x}} } \over {5 + {{1}\over{x}} } }  } \over { 7 + {{2}\over{x}} } } &\xrightarrow{either} &&{ { {{5 \cdot {{1}\over{x}} } \over {5 + {{1}\over{x}} } } \cdot \color{blue}{{| \cdot x}\over{| \cdot x}} } \over { 7 + {{2}\over{x}} } } && = { { {{5 } \over {5x + 1 } } } \over { 7 + {{2}\over{x}} } } \\ &\xrightarrow{\quad or \quad} &&{ { {{5 \cdot {{1}\over{x}} } \over {5 + {{1}\over{x}} } } } \over { 7 + {{2}\over{x}} } } \cdot \color{blue}{{| \cdot x}\over{| \cdot x}} = { { {{5 \cdot {{1}\over{x}} } \over {5 + {{1}\over{x}} } } \cdot \color{blue}{{| \cdot x}\over{ }} } \over { 7 + {{2}\over{x}} } } \cdot \color{blue}{{ }\over{| \cdot x}} && = { { {{5 } \over {5 + {{1}\over{x}} } } } \over { 7x + 2 } } \end{align*} \\ So please never never multiply in such cases all numerators and denominator with the factor...
   * Rearrange fractions correct: based on $\beta = {{I_C}\over{I_B}}$ on **cannot** derive $I_B = {{\beta}\over{I_C}}$..   * Rearrange fractions correct: based on $\beta = {{I_C}\over{I_B}}$ on **cannot** derive $I_B = {{\beta}\over{I_C}}$..
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 ===== Do physics right ===== ===== Do physics right =====
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     * impedances are not (only) resistors, at least do not think of $R$ is given as $\underline{Z}$. \\ For purely ohmic components the other way around is correct: $\underline{Z}=R$.     * impedances are not (only) resistors, at least do not think of $R$ is given as $\underline{Z}$. \\ For purely ohmic components the other way around is correct: $\underline{Z}=R$.
     * However, impedances 'act' like ohmic resistors in formulars. \\ E.g. for the series circuit: $R_{eq}=R_1+R_2+R_3+... \rightarrow \underline{Z}_{eq}=\underline{Z}_1+\underline{Z}_2+\underline{Z}_3+... $     * However, impedances 'act' like ohmic resistors in formulars. \\ E.g. for the series circuit: $R_{eq}=R_1+R_2+R_3+... \rightarrow \underline{Z}_{eq}=\underline{Z}_1+\underline{Z}_2+\underline{Z}_3+... $
 +  * A resistor does not have a continuous line through: \\ {{drawio>exam_infos:wrongresistor.svg}} 
   * circuits have to be closed, at least with giving voltages with arrows. \\ So, the in the following imgage the left side circuit is not correct: \\ {{drawio>exam_infos:wrongcircuit.svg}}    * circuits have to be closed, at least with giving voltages with arrows. \\ So, the in the following imgage the left side circuit is not correct: \\ {{drawio>exam_infos:wrongcircuit.svg}}