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A radio can tune over the frequency range of a portion of MW broadcast band:

Q7.10  A radio can tune over the frequency range of a portion of MW broadcast band:  (800kHz\: to1200kHz)  . If its LCcircuit has an effective inductance of 200\mu H, what must be the range of its variable capacitor?

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Given, 

Range of the frequency in which radio can be tune = (800kHz\: to1200kHz)

The effective inductance of the Circuit = 200\mu H

Now, As we know,

 w^2=1/\sqrt{LC}

C=1/w^2L

where w is tuning frequency.

For getting the range of the value of a capacitor, let's calculate the two values of the capacitor, one maximum, and one minimum.

first, let's calculate the minimum value of capacitance which is the case when tuning frequency = 800KHz.

C_{minimum}=\frac{1}{w_{minimum}^2L}=\frac{1}{(2\pi(800*10^3))^2*200*10^{-6}}=1.981*10^{-10}F

Hence the minimum value of capacitance is 198pF.

Now, Let's calculate the maximum value of the capacitor.

in this case, tuning frequency = 1200KHz

C_{maximum}=\frac{1}{w_{maximum}^2L}=\frac{1}{(2\pi(1200*10^3))^2*200*10^{-6}}=88.04*10^{-12}F

Hence the maximum  value of the capacitor is 88.04pf

Hence the Range of the values of the capacitor is 88.04pF to 198.1pF.

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