please answer in units of pC. You are designing a radio receiver based on the id

Question

please answer in units of pC.

You are designing a radio receiver based on the idea of a series LRC circuit as shown be low. The two major radio stations in town are KUT and KMFA, which broadcast at frequencies 94.2 MHz and 93.2 MHz. respectively. Electromagnetic signals from these radio stations simultaneously supply sinusoidal emfs to the circuit via an antenna. The receiving circuit includes an inductor of 0.55 MuH. a variable capacitor C, and a speaker whose resistance you must choose. At what value of the variable capacitance C will the sound volume (i.e., the power dissipated in the speaker) be maximum for KUT?

Explanation / Answer

Resonant frequency is given by :

fr = (1/(2*pi))*(1/sqrt(L*C))

Now,

here L = 0.55 uH = 0.55*10^-6 H

For, KUT, fr = 94.2 MHz = 94.2*10^6 Hz

So, 94.2*10^6 = (1/(2*pi))*(1/sqrt(0.55*10^-6*C))

So, C = 5.2*10^-12 F = 5.2 pF <-------answer

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