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fix: slide overlap

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Matthias Jung
2026-05-16 13:45:53 +02:00
parent 082276dba0
commit 53c060893c
1 changed files with 14 additions and 6 deletions
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contents/slides/reihe_parallel_widerstandsnetz_2.md
+14 -6
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@@ -23,9 +23,11 @@ $I = I_2 + I_3 = \qty{1}{\milli\ampere} + \qty{1}{\milli\ampere} = \qty{2}{\mill
<fragment>
$U = R_{\mathrm{ges}} \cdot I = \qty{15}{\kilo\ohm} \cdot \qty{2}{\milli\ampere} = \qty{30}{\volt}$
</fragment>
---
[question:AD107]
---
#### Lösungsweg
* gegeben: $R_1 = R_2 = R_3 = \qty{10}{\kilo\ohm}$
* gegeben: $U=\qty{15}{\volt}$
@@ -34,12 +36,15 @@ $U = R_{\mathrm{ges}} \cdot I = \qty{15}{\kilo\ohm} \cdot \qty{2}{\milli\ampere}
<fragment>
$R_{\mathrm{ges}} = R_1 + \frac{R_1 \cdot R_2}{R_1 + R_2} = \qty{10}{\kilo\ohm} + \frac{\qty{10}{\kilo\ohm} \cdot \qty{10}{\kilo\ohm}}{\qty{10}{\kilo\ohm} + \qty{10}{\kilo\ohm}} = \qty{15}{\kilo\ohm}$
</fragment>
<fragment>
$\frac{U_3}{U} = \frac{R_2 \parallel R_3}{R_{\mathrm{ges}}} \Rightarrow U_3 = \frac{R_2 \parallel R_3}{R_{\mathrm{ges}}} \cdot U = \frac{\qty{5}{\kilo\ohm}}{\qty{15}{\kilo\ohm}} \cdot \qty{15}{\volt} = \qty{5}{\volt}$
</fragment>
<fragment>
$I_3 = \frac{U_3}{R_3} = \frac{\qty{5}{\volt}}{\qty{10}{\kilo\ohm}} = \qty{0,5}{\milli\ampere}$
</fragment>
---
[question:AD108]
---
@@ -51,33 +56,36 @@ $I_3 = \frac{U_3}{R_3} = \frac{\qty{5}{\volt}}{\qty{10}{\kilo\ohm}} = \qty{0,5}{
<fragment>
$\frac{U_2}{U} = \frac{R_2 \parallel R_3}{R_{\mathrm{ges}}} \Rightarrow U_2 = \frac{R_2 \parallel R_3}{R_{\mathrm{ges}}} \cdot U = \frac{\qty{5}{\kilo\ohm}}{\qty{15}{\kilo\ohm}} \cdot \qty{15}{\volt} = \qty{5}{\volt}$
</fragment>
<fragment>
$P_2 = \frac{U_2^2}{R_2} = \frac{(\qty{5}{\volt})^2}{\qty{10}{\kilo\ohm}} = \qty{2,5}{\milli\watt}$
</fragment>
---
[question:AD109]
---
--- style="font-size: 0.7em;"
#### Lösungsweg
<left>
* gegeben: $R = \qtyrange{0}{1}{\kilo\ohm}$
* gegeben: $R_1 = \qty{200}{\ohm}$
</left>
<right>
* gegeben: $R_2 = \qty{100}{\ohm}$
* gegeben: $R_3 = \qty{200}{\ohm}$
</left>
<right>
$R_{\mathrm{ges}} = R_1 + \frac{R_2 \cdot (R_3 + R)}{R_2 + (R_3 + R)}$
</right>
<fragment>
$R_{\mathrm{ges}} = R_1 + \frac{R_2 \cdot (R_3 + R)}{R_2 + (R_3 + R)}$
</fragment>
<fragment>
Bei $R = \qty{0}{\ohm}$:
$R_{\mathrm{ges}} = \qty{200}{\ohm} + \frac{\qty{100}{\ohm} \cdot (\qty{200}{\ohm} + \qty{0}{\ohm})}{\qty{100}{\ohm} + \qty{200}{\ohm} + \qty{0}{\ohm}} \approx \qty{267}{\ohm}$
</fragment>
<fragment>
Bei $R = \qty{1}{\kilo\ohm}$:
$R_{\mathrm{ges}} = \qty{200}{\ohm} + \frac{\qty{100}{\ohm} \cdot (\qty{200}{\ohm} + \qty{1}{\kilo\ohm})}{\qty{100}{\ohm} + \qty{200}{\ohm} +\qty{1}{\kilo\ohm}} \approx \qty{292}{\ohm}$
</fragment>
---
[question:AD110]
---