The range of capacitance values that are needed so the antenna can pick up all the radio waves broadcasted by FM stations is from 5.45 x 10⁻¹² H to 3.62 x 10⁻¹² H.
The frequency at which the antenna can pick the radio waves broadcasted is known as resonance frequency.
At resonance frequency, the capacitive reactance is equal to inductive reactance.
Xc = Xl
[tex]\frac{1}{2\pi fC} = 2\pi fL\\\\4\pi^2 f^2 LC = 1\\\\C = \frac{1}{4\pi^2 f^2L}[/tex]
where;
When the frequency is 88 MHz, the capacitance is;
[tex]C = \frac{1}{4\pi^2 \times (88 \times 10^6)^2 \times (6\times 10^{-7})} \\\\C = 5.45 \times 10^{-12} \ H\\\\[/tex]
When the frequency is108 MHz, the capacitance is;
[tex]C = \frac{1}{4\pi^2 \times (108 \times 10^6)^2 \times (6\times 10^{-7})} \\\\C = 3.62\times 10^{-12} \ H\\\\[/tex]
Thus, the range of capacitance values that are needed so the antenna can pick up all the radio waves broadcasted by FM stations is from 5.45 x 10⁻¹² H to 3.62 x 10⁻¹² H.
Learn more about resonance frequency here: https://brainly.com/question/9324332
