Question 263: AC fundamentals

Question

Figure shows the combination of inductances and capacitances. Resonant frequency of the $\mathrm{L}-\mathrm{C}$ circuit is

Accepted Answer

Inductors: L and 2 L are in series
$	herefore \quad \mathrm{L}_{\mathrm{eq}}=\mathrm{L}+2 \mathrm{~L}=3 \mathrm{~L}$
Capacitors: C and 2 C are in parallel
$	herefore \quad \mathrm{C}_{\mathrm{eq}}=\mathrm{C}+2 \mathrm{C}=3 \mathrm{C}$
Resonant Frequency:
$$ \begin{aligned} \mathrm{f} & =\frac{1}{2 \pi \sqrt{\mathrm{~L}_{	ext {eq }} \mathrm{C}_{	ext {eq }}}}=\frac{1}{2 \pi \sqrt{(3 \mathrm{~L})(3 \mathrm{C})}} \ 	herefore \quad \mathrm{f} & =\frac{1}{6 \pi \sqrt{\mathrm{LC}}} \end{aligned} $$

Answer

$\frac{1}{2 \pi \sqrt{\mathrm{LC}}}$

Answer

$\frac{1}{3 \pi \sqrt{\mathrm{LC}}}$

Answer

$\frac{1}{4 \pi \sqrt{\mathrm{LC}}}$

Answer

$\frac{1}{6 \pi \sqrt{\mathrm{LC}}}$.

AC fundamentals

Figure shows the combination of inductances and capacitances. Resonant frequency of the \mathrm{L}-\mathrm{C} circuit is

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