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?

Answers (1)

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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