The tuning circuit of an AM radio contains an L C...

The tuning circuit of an AM radio contains an $L C$ combination. The inductance is $0.200 \mathrm{mH},$ and the capacitor is variable, so that the circuit can resonate at any frequency between $550 \mathrm{kHz}$ and $1650 \mathrm{kHz}$. Find the range of values required for $C.$

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Key Concepts

LC Resonant Circuits

An LC resonant circuit consists of an inductor (L) and a capacitor (C) that together form a system capable of oscillating at a particular frequency. This frequency occurs when the reactance of the inductor exactly cancels the reactance of the capacitor, resulting in a condition known as resonance, where the circuit naturally selects and favors a specific frequency.

Resonance Frequency Formula

The resonant frequency of an LC circuit is given by the formula f = 1/(2??(LC)). This equation shows the inverse relationship between the resonant frequency and the square root of the product of the inductance and capacitance. It is a central tool in designing circuits such as those in radio receivers, where the desired frequency is set by carefully choosing or varying component values.

Frequency Tuning with Variable Components

In applications like AM radio, a variable capacitor is used in combination with a fixed inductor to allow the tuning of the circuit over a range of frequencies. By varying the capacitance, the resonant frequency of the LC circuit can be adjusted, enabling the receiver to select different channels within the available frequency spectrum.

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