The figure shows a combination of inductances | vedclass

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(D) In the given circuit,the two inductors $L$ and $2L$ are connected in series. Therefore,the equivalent inductance $L_{eq}$ is given by:$L_{eq} = L

Vedclass · Accepted Answer

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

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(D) In the given circuit,the two inductors $L$ and $2L$ are connected in series. Therefore,the equivalent inductance $L_{eq}$ is given by:$L_{eq} = L + 2L = 3L$The two capacitors $C$ and $2C$ are connected in parallel. Therefore,the equivalent capacitance $C_{eq}$ is given by:$C_{eq} = C + 2C = 3C$The resonant frequency $f$ of an $L-C$ circuit is given by the formula:$f = \frac{1}{2 \pi \sqrt{L_{eq} C_{eq}}}$Substituting the values of $L_{eq}$ and $C_{eq}$ into the formula:$f = \frac{1}{2 \pi \sqrt{(3L)(3C)}}$$f = \frac{1}{2 \pi \sqrt{9LC}}$$f = \frac{1}{2 \pi \cdot 3 \sqrt{LC}}$$f = \frac{1}{6 \pi \sqrt{LC}}$

The figure shows a combination of inductances and capacitances. The resonant frequency of the $L-C$ circuit is:

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