An A.C. circuit contains a resistor 'R', an inductor 'L' and a capacitor 'C' connected in series. When it is connected to an A.C. generator of fixed output voltage and variable frequency, the current in the circuit is found to be leading the applied voltage `pi//4` rad, when the frequency is `f_(1)`. When the frequency of the generator increased to `'f_(2)'` the current is found to be lagging behind the applied voltage by `pi//4` rad. The resonant frequency of the circuit is

Options

A. `(f_1 f_2)/( f_1 +f_2)`
B. `(f_1 +f_2)/(2)`
C. `(2f_1 f_2)/( f_1 +f_2)`
D. `sqrt(f_1 f_2)`

Answer

D