The natural frequency of the circuit shown in the figure is

Options

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

Answer

A

Explanation

`L_(eq) = L + L = 2 L`
`C_(eq) = (C_(1) C_(2))/(C_(1) + C_(2)) = (C^(2))/(2C) = (C )/(2)`
`f = (1)/(2 pi sqrt(L_(eq)C_(eq))) = (1)/(2 pi sqrt(2 L xx (C )/(2))) = (1)/(2 pi sqrt(LC))`