When you turn the dial on a radio to tune it, you are...

When you turn the dial on a radio to tune it, you are adjusting a variable capacitor in an LC circuit. Suppose you tune to an AM station broadcasting at a frequency of $1000 . \mathrm{kHz}$, and there is a $10.0-\mathrm{mH}$ inductor in the tuning circuit. When you have tuned in the station, what is the capacitance of the capacitor?

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Key Concepts

LC Circuit

An LC circuit is a type of electrical circuit that consists of an inductor (L) and a capacitor (C) connected together. It is a fundamental configuration in electronics that oscillates at a natural resonant frequency due to the exchange of energy between the magnetic field of the inductor and the electric field of the capacitor.

Resonant Frequency

The resonant frequency of an LC circuit is the specific frequency at which the circuit naturally oscillates with maximum amplitude. It is determined by both the inductance and the capacitance and is given by the formula f = 1/(2??(LC)). This concept is crucial for tuning circuits, as it allows the circuit to select a specific frequency while rejecting others.

Variable Capacitor

A variable capacitor is a capacitor whose capacitance can be adjusted. This adjustability is used to fine-tune the resonant frequency of an LC circuit, for example in radio receivers, by changing the capacitance value to match the frequency of the desired signal. This makes it possible to selectively receive different broadcast frequencies.

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