HI, could you please answer part B ? A television channel is assigned the freque

Question

HI, could you please answer part B ?

A television channel is assigned the frequency range from 53 MHz to 59 MHz. A series RLC tuning circuit in a TV receiver resonates in the middle of this frequency range. The circuit uses a 18 pF capacitor.

(a) What is the value of the inductor?
.449 µH

(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?

I tried 9.29 ohms but that was wrong..

Explanation / Answer

Let voltage be V.
current at resonant frequency = V/R

at 53 MHz,
xL = 2*pi*f*L = 2*pi*53*10^6*(0.449*10^-6) = 149.52 ohm
Xc = 1/(2*pi*f*C) = 1/ (2*pi*53*10^6 * 18*10^-12) = 166.83 ohm
net Z = sqrt (R^2 + (166.83-149.52)^2) = sqrt (R^2 + 299.64)
At this f,
current = 0.5 * current at resonant frequency
so,
V/ sqrt (R^2 + 299.64) = 0.5 * V/R
2R = sqrt (R^2 + 299.64)
4R^2 = R^2 + 299.64
R = 10 ohm

Answer: 10 ohm

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