A television channel is assigned the frequency range from 54 MHz ...

Question

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.a. What is the value of the inductor?

Accepted Answer

Hello little fellow physicists today, we're gonna solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use. In order to solve this problem. A band pass filter formed by a series RLC operates between a minimum frequency equal to 500 Hertz to a maximum frequency equal to 5.0 kg Hertz. The renaissance frequency of this band pass filter is equal to the average of its minimum and maximum frequencies calculate the capacitance required for the filter given an inductance of 100 milli Henry. OK. So we're given some multiple choice answers here. Let's read them off to see what our final answer might be. A is 33 nano Ferres B is 78 nano Ferres. C is 1.2 micro Ferris and D is 4.0 micro Ferres. OK. So our end goal is to calculate the capacitance required for the filter given an inductance of 100 milli Henry. OK. So in order to determine the capacitance for the filter, we must first find the resonance frequency which is the average of the minimum and maximum frequency frequencies which is written as F subscript zero. And let's call it equation one. So F subscript zero is equal to F subscript men. So the minimum frequency plus the maximum frequency F subscript max divided by two. So let's plug in our known variables. And so for excuse me, software F zero. OK. So the minimum frequency was hurts plus the max maximum frequency which was 5.0 kilohertz. But let's convert that to Hertz. So it's 5.0 multiplied by 10 to the power of three Hertz divided by two. So when we plug that into a calculator, we should get 2.75 killer hurts. A. So note that the renaissance resonance frequency in a RLC circuit occurs when the inductive and capacitive resist reactants in the circuit cancel each other out which results in a purely resistive impedance. So now we need to use the resonance frequency and the inductance to determine the capacitance by using the formula for capacitance, which the formula for capacitance states that the capacitance is equal to one divided by four pi squared multiplied by F subscript zero squared multiplied by I where I is the inductance. OK. So now we can plug in all of our known variables to solve for the capacitance. So let's do that. So one divided by four pi square multiplied by F zero, which we discovered to be two point 75 kilohertz. But we need to convert that to Hertz. So it's multiplied by 10 to the power of three Hertz. So we can write that up here to remember. OK. Squared, multiplied by the impedance which the impedance or I should say correction, the inductance. So the inductance was given to us as 100 milla Henry, but we need to convert Millah Henry to Henry's. So we take then multiply it by 10 to the power of negative three to get it from Mila Henry's to Henry's. Ok. So when we plug that into a calculator, we should get 3. multiplied by 10 to the power of negative eight F ads. But we need to multiply that by 10 to the power of nine to get it in nano Ferrat. So when we do that, we should get 33 nano ferrets, which is our final answer for the capacitance. Awesome. So we did it we saw for our final answer. So going back to look at our multiple choice answers, that means the correct answer is a 33 nano ferrets. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

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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.a. What is the value of the inductor?

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