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This is a simple texbook problem: 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 19 pF capacitor. (a) What is the value of the inductor? (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? (Hint: when you calculate the current amplitude at 54 and 60 MHz, it should be 50% of the current amplitude at 57 MHz).

I have figured our (a) and most of (b). For (b) I obtain the equation $R=\frac{1}{\sqrt{3}}(\omega{L}-\frac{1}{\omega{C}})$. At this point I understand I need to sub in the boundary frequencies of 54 and 60 MHz. However, I fail to understand why the "minimum resistance" should be taken from the substitution of the lower bound frequency of 54MHz and not 60 MHz.

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The response isn't exactly symmetric about 57 MHz and will be slightly lower at 54 MHz than 60 MHz. So the critical minimum series resistance will be slightly larger when calculated at 54 MHz rather than 60 MHz. The difference becomes negligible if the bandwith is very narrow.

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