The natural frequency of the circuit shows in Fig. is

Options

A. `(1)/(2 pi sqrt(LC))`
B. `(1)/(2 pi sqrt(2LC))`
C. `(2)/(2 pi sqrt(LC))`
D. none of these

Answer

A

Explanation

In Fig., the two condensers are in series and so are the two inductors.
Therefore, `L_(s) = L + L = 2 L`
`(1)/(C_(s)) = (1)/(C ) + (1)/(C ) = (2)/(C ) , C_(s) = C//2`
`:.` Natural frequency of the circuit,
`v = (1)/(2 pi sqrt(L_(s) C_(s))) = (1)/(2 pi sqrt(2 L xx C //2)) = (1)/(2 pi sqrt(LC))`