Figure shows an inductance L and a parallel plate capacitor of width w = 20 cm and thickness 0.2 cm. A dielectric with dielectric constant κ = 4.8 that can completely fill the space between the capacitor plates can be slid between the plates. The inductor has an inductance L = 2 mH. When half the dielectric is between the capacitor plates, i.e., when x = ½w, the resonant frequency of this LC combination is 90 MHz.

(a) What is the capacitance of the capacitor without the dielectric?

(b) Find the resonance frequency as a function ofx.

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