Radio receivers are usually tuned by adjusting the capacitor of an lc circuit. if c = c1 for a frequency of 600 khz, then for a frequency of 1200 khz c must be adjusted to what value?

Explanation:

Given:

Initial capacitance, C = C₁

Initial Frequency, F₁ = 600kHz

Final Frequency, F₂ = 1200kHz

let the adjusted capacitance be, C₂

Now

the  frequency (f) is given as:

where, L = inductance (same for the same material)

thus substituting the values we have

    ...............(1)

and

       ..............(2)

dividing the equation 1 with 2, we get

or

or

or

hence, the new capacitance C, must be one-fourth times the initial capacitance

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