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Q.

Two series resonant circuits with component values L₁, C₁ and L₂, C₂ respectively have the same resonant frequency. They are then connected in series ; the resonant frequency of the combination is :

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a

$\frac{1}{2 π \sqrt{L_{1} C_{1}}}$

b

$\frac{1}{2 π \sqrt{L_{2} C_{2}}}$

c

$\frac{1}{2 π \sqrt{(L_{1} + L_{2}) (C_{1} + C_{2})}}$

d

$\frac{1}{2 π \sqrt{L_{1} C_{2}}}$

answer is A.

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Detailed Solution

$\begin{array}{l} ω = \frac{1}{\sqrt{L_{1} C_{1}}} = \frac{1}{\sqrt{L_{2} C_{2}}} \Rightarrow L_{1} C_{1} = L_{2} C_{2} \\ L_{eq} = L_{1} + L_{2} \\ C_{eq} = (\frac{C_{1} C_{2}}{C_{1} + C_{2}}) \\ ω_{e q} = \frac{1}{\sqrt{L_{e q} C_{e q}}} \end{array}$

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