A series LCR circuit has a resonant frequency f₀ . The capacitor in the circuit is a parallel plate capacitor with air between its plates. If the distance between the plates of the capacitor is halved and the space between them is completely filled with a dielectric material of dielectric constant K = 2 , the new resonant frequency of the circuit will be:

Step-by-step solution

The initial resonant frequency of the LCR circuit is f₀ = 1 2 LC . The initial capacitance of the air-filled parallel plate capacitor is C = ₀ A d . When the distance between the plates is halved ( d' = d 2 ) and a dielectric of K = 2 is introduced, the new capacitance becomes: C' = K ₀ A d' = 2 ₀ A ( d 2 ) = 4 ₀ A d = 4C . The new resonant frequency is f'₀ = 1 2 LC' = 1 2 L(4C) = 1 2 ( 1 2 LC ) = f₀ 2 . Answer: f₀ 2