The LC series resonant circuit produces a resonant frequency ' f '. If L is tripled and 'C' is increased by 3C, the resonant frequency will be

Step-by-step solution

The resonant frequency of an LC series circuit is given by f = 1 2 LC . Given that the inductance L is tripled, the new inductance is L' = 3L . The capacitance C is increased by 3C , so the new capacitance is C' = C + 3C = 4C . The new resonant frequency f' is given by: f' = 1 2 L'C' Substituting the values of L' and C' : f' = 1 2 (3L)(4C) = 1 2 12LC f' = 1 2 3 ( 1 2 LC ) f' = f 2 3 Answer: f 2 3