A series resonant circuit consists of an inductor 'L' and capacitor 'C' which produces resonant frequency 'f'. If 'L' is increased by '2L' and 'C' is changed to '9C' the resonant frequency will be

Step-by-step solution

The resonant frequency of a series L-C circuit is given by: f = 1 2 LC Given that the inductance is increased by 2L , the new inductance is: L' = L + 2L = 3L The capacitance is changed to 9C , so the new capacitance is: C' = 9C The new resonant frequency f' is: f' = 1 2 L'C' Substituting the values of L' and C' : f' = 1 2 (3L)(9C) f' = 1 2 27LC f' = 1 3 3 ( 1 2 LC ) f' = f 3 3 Answer: f 3 3