Problem 35.60 A television channel is assigned the frequency range from 54 MHz t

Question

Problem 35.60

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?

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?

Problem 35.60

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?

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?

Explanation / Answer

mid point of 54 and 60 hz is 57 Hz

at resosnace W^2 = 1/LC

inductance L = 1/w^2C

W = 2pi f = 2*3.14 * 57 *10^6 = 3.58*10^8 rad/s

so L = 1/(3.58*10^8 * 3.58 *10^8 * 16 *10^-12)

L = 487.6 nH

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it doesnot depends on Resistance

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