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fix: use X_L and X_C instead of X_{\mathrm{L}} and X_{\mathrm{C}}

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`L` and `C` are regular equation symbols. There is no need to set it upright.
This commit is contained in:
Mario Haustein
2026-02-22 17:56:49 +01:00
parent 4d49ee4e39
commit aca81684c1
1 changed files with 2 additions and 2 deletions
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contents/slides/reihe_parallel_gemischt.md
+2 -2
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@@ -49,7 +49,7 @@ Einheitenpräfixe beachten und mit Kehrwerten rechnen
* gesucht: $Z$
<fragment>
$\begin{split} X_{\textrm{L}} &= \omega \cdot L = 2 \cdot \pi \cdot f \cdot L\\ &= 2 \cdot \pi \cdot \qty{1}{\mega\hertz} \cdot \qty{100}{\micro\henry} = \qty{628}{\ohm}\end{split}$
$\begin{split} X_L &= \omega \cdot L = 2\pi \cdot f \cdot L\\ &= 2\pi \cdot \qty{1}{\mega\hertz} \cdot \qty{100}{\micro\henry} = \qty{628}{\ohm}\end{split}$
</fragment>
<fragment>
$Z = \sqrt{R^2 + X^2} = \sqrt{(\qty{100}{\ohm})^2 + (\qty{628}{\ohm})^2} \approx \qty{636}{\ohm}$
@@ -66,7 +66,7 @@ $Z = \sqrt{R^2 + X^2} = \sqrt{(\qty{100}{\ohm})^2 + (\qty{628}{\ohm})^2} \approx
* gesucht: $Z$
<fragment>
$\begin{split} X_{\textrm{C}} &= \frac{1}{\omega \cdot C} = \frac{1}{2 \cdot \pi \cdot f \cdot C}\\ &= \frac{1}{2 \cdot \pi \cdot \qty{1}{\mega\hertz} \cdot \qty{100}{\nano\farad}} = \qty{159}{\ohm}\end{split}$
$\begin{split} X_C &= \frac{1}{\omega \cdot C} = \frac{1}{2\pi \cdot f \cdot C}\\ &= \frac{1}{2\pi \cdot \qty{1}{\mega\hertz} \cdot \qty{100}{\nano\farad}} = \qty{159}{\ohm}\end{split}$
</fragment>
<fragment>
$Z = \sqrt{R^2 + X^2} = \sqrt{(\qty{100}{\ohm})^2 + (\qty{159}{\ohm})^2} \approx \qty{188}{\ohm}$