FM radio stations use radio waves with frequencies from 88.0 to 108 MHz to broadcast their signa

step 1 In this problem, I can write the minimum capacitance of the capacitor as C minimum is equal to 1

FM radio stations use radio waves with frequencies from 88.0...

FM radio stations use radio waves with frequencies from 88.0 to $108 \mathrm{MHz}$ to broadcast their signals. Assuming that the inductance in Figure $24-5$ has a value of $6.00 \times 10^{-7} \mathrm{H}$ determine the range of capacitance values that are needed so the antenna can pick up all the radio waves broadcasted by FM stations.

Key Concepts

LC Circuits

An LC circuit is a fundamental electrical circuit consisting of an inductor (L) and a capacitor (C) connected together. These circuits naturally oscillate at a frequency determined by the component values due to the continuous exchange of energy between the capacitor's electric field and the inductor's magnetic field. LC circuits are widely used in radio technology for filtering and tuning applications.

Resonant Frequency Formula

The resonant frequency of an LC circuit is determined by the relationship f = 1/(2??(LC)). This formula is central in circuit design because it links the inductance and capacitance directly to the frequency at which the circuit will most efficiently oscillate. By adjusting either the capacitance or inductance, designers can tune the circuit to resonate at a desired frequency, making it a versatile tool for selecting specific radio frequencies.

Capacitance Tuning in Receiver Circuits

In radio receivers, especially those used for FM broadcasting, it is often necessary to cover a range of frequencies. With a fixed inductor value, varying the capacitance allows the circuit to tune across different frequencies within the FM band. By applying the resonant frequency formula, one can determine the required range of capacitance values that will enable the receiver to match the desired broadcast frequencies, ensuring efficient signal reception.

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