The FM radio band covers the frequency range 88-108 MHz If the variable capacitor in an FM recei

step 1 Well, frequency is equal to 88 to 108 megahertz, and this is the range of frequency. And capacit

The FM radio band covers the frequency range 88-108 MHz If...

The FM radio band covers the frequency range $88-108 \mathrm{MHz}$ If the variable capacitor in an FM receiver ranges from $10.9 \mathrm{pF}$ to $16.4 \mathrm{pF}$, what inductor should be used to make an $L C$ circuit whose resonant frequency spans the FM band?

Key Concepts

Component Selection Based on Desired Frequency Range

When designing a resonant circuit to cover a specific frequency range, the values of the circuit components such as the inductor and capacitor must be carefully selected. Knowing the desired frequency limits and using the resonant frequency formula allows engineers to compute an appropriate inductor value that, in combination with a variable capacitor, can span the required frequency band.

LC Circuit

An LC circuit is an electrical circuit consisting of an inductor (L) and a capacitor (C) connected together. It is a basic resonant circuit or tank circuit that can oscillate at a specific frequency without any external signal, due to the exchange of energy between the magnetic field of the inductor and the electric field of the capacitor.

Resonant Frequency Formula

The resonant frequency of an LC circuit is determined by the formula f = 1/(2??(LC)), where f is the frequency, L is the inductance, and C is the capacitance. This formula shows that the resonant frequency is inversely proportional to the square root of the product of the circuit’s inductance and capacitance.

Frequency Band

A frequency band represents a specified range of frequencies within the electromagnetic spectrum. In many applications, devices must be designed to operate within a given band, which requires careful tuning of circuit components so that the overall resonant frequency covers the desired range.

Variable Capacitance Tuning

Variable capacitors are used in tuning circuits to adjust the resonant frequency. By changing the capacitance value in an LC circuit, the resonant frequency can be shifted within a desired range. This principle is commonly used in radio receivers to select different broadcast frequencies.

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