\( f_0 = \frac{1}{2 \pi \sqrt{L C}} \quad \rightarrow C=? \)
\( f_0 = 460 \mathrm{kHz} \)
\( L=50 \mu H \)
\( f_0 : 2 \pi \sqrt{LC} =1 \)
\( \sqrt{LC} = \frac{1}{f_0 \cdot 2 \pi} \quad | (...)^2 \)
\( LC = \frac{1}{( f_0 \cdot 2 \pi )^2} \quad | :L \)
\( C = \frac{1}{L·( f_0 \cdot 2 \pi )^2} \)
\( C=\frac{1}{50_{\mu H} \cdot\left(460 \mathrm{kHz} · 2 \pi \right)^{2}} \)
\( C = \frac{1}{ 50 · \cancel{ 10^{-6} } · \frac{VS}{A} · \frac{1}{s^2} 11600 · \cancel{ 10^6 } · 4 \pi^2} \)
\( C=\frac{1}{50 · 2 11600 · 4 \pi^{2}} F \)
\( C ≈ 2,39 nF \)