The "over-the-air" television channel 6 operates between frequencies 82 MHz and 88 MHz, with the video and audio using different parts of this frequency range. To watch (and listen) to the channel properly, the tuner circuit in a television must resonate in the middle of this range (85 MHz) andproduce a current over the whole range of at least 50% of the peak current at resonant frequency. A particular television tuning circuit is built with a 18.1 pF capacitor, a variable inductor, and a variable resistor. What value should the resistor be in order for the current at both 82 MHz and 88 MHz to be at least 50% of the current at the resonant frequency? Hint:You'll have to first calculate the value of the inductor so that the television tunes to channel 6.

University Physics Volume 2
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Chapter15: Alternating-current Circuits
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The "over-the-air" television channel 6 operates between frequencies 82 MHz and 88 MHz, with the video and audio using different parts of this frequency range. To watch (and listen) to the channel properly, the tuner circuit in a television must resonate in the middle of this range (85 MHz) andproduce a current over the whole range of at least 50% of the peak current at resonant frequency.

A particular television tuning circuit is built with a 18.1 pF capacitor, a variable inductor, and a variable resistor. What value should the resistor be in order for the current at both 82 MHz and 88 MHz to be at least 50% of the current at the resonant frequency?

Hint:You'll have to first calculate the value of the inductor so that the television tunes to channel 6.

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