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

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west