# TV Channel Frequency Range Question [closed]

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.