A series LCR circuit has a resonant frequency f₀ . If the inductance of the circuit is doubled and the capacitance is reduced to one-eighth of its original value, the new resonant frequency of the circuit will be :

Step-by-step solution

The initial resonant frequency of the series LCR circuit is given by: f₀ = 1 2 LC When the inductance is doubled ( L' = 2L ) and the capacitance is reduced to one-eighth ( C' = C 8 ), the new resonant frequency f' is: f' = 1 2 L'C' Substituting the new values: f' = 1 2 2L C 8 f' = 1 2 LC 4 f' = 2 2 LC f' = 2f₀ Thus, the new resonant frequency is 2f₀ . Answer: 2f₀