A television channel is assigned the frequency range from 54 MHz to 60 MHz. A se

Question

A television channel is assigned the frequency range from 54 MHz to 60 MHz. A series RLC tuning circuit in a TV receiver resonates in the middle of this frequency range. The circuit uses a 16 pF capacitor.

Part A ) What is the value of the inductor? (in µH)


Part B) In order to function properly, the current throughout the frequency range must be at least 50% of the current at the resonance frequency. What is the minimum possible value of the circuit's resistance? (in O)

I've tried the problem a few times with no luck so far I'm not entirely sure what im doing wrong so a detailed explaination if possible would be greatly appreciated. Thank you in advance.

Explanation / Answer

A) f = 54+60/2 = 57e6 Hz w = 2*3.14*f = 2*3.14*57 = 357.96e6 rad/s w = (1/LC)^0.5 >>> L = 1/(w^2 * C) = 1/(357.96*357.96*16) = 0.488 uH B) I2 / I1 = Z1/Z2 >>>> 0.5 = Z1/Z2 >>>> Z2 = 2 Z1 At resonance frequency, impedance is R: Z2 = 2 * Z1 >>>> Z2^2 = 4 * R^2 >>>> R^2 + (XL - XC)^2 = 4 * R^2 >>>> (XL - XC)^2 = 3 * R^2 >>>> 2*3.14*f*L - 1/(2*3.14*f*C) = 3^0.5 * R >>>> 2*3.14*60e6*0.488e-6 - 1/(2*3.14*60e6*16e-12) = 3^0.5 * R >>>> R = 10.40 ohm >>>> 2*3.14*54e6*0.488e-6 - 1/(2*3.14*54e6*16e-12) = 3^0.5 * R >>>> R = 10.86 ohm final answer is R = 10.40 ohm

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