You are making a radio that recieves a signal of 93.4 MHz. You want to make this

Question

You are making a radio that recieves a signal of 93.4 MHz. You want to make this receiver out of an LRC circuit that has a capacitor with a capacitance of 2.90x10^(-12) F and an inductor with an inductance of 1.00x10^(-6) H.

There are two specific specifications:
i) Your receiver gives the maximum power response to the 93.4 MHz signal

ii) The average power delivered to the resistor in reponse to the 93.3 MHz broadcast is 1.00% the average power delivered to 93.4 MHz.

In order to receive 5 stars the work must be shown with the answer.

Big thanks to everyone in advance!

Explanation / Answer

a)for max power w = 1/sqrt(LC)

==> C = 1/w^2L = 1/((93.4*10^6)^2*1*10^-6) = 1.146 E-10 F

b)V^2/sqrt(R^2+(wL-1/wC)^2) = 0.01*V^2/R

==> 0.01*sqrt(R^2+(wL-1/wC)^2) = R

==> R^2 +(wL-1/wC)^2 = 10000R^2

==> R = sqrt((wL-1/wC)^2/9999)

(wL-1/wC)^2 = {(93.3*10^6*1*10^-6) - (1/(93.3*10^6*1.146*10^-10))}^2 =0.05121

so R = sqrt( 0.05121/9999)=0.00226 ohms

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