An R L C circuit is used in a radio to tune into an FM station broadcasting at f=99.7 MHz . The

step 1 Well, frequency F is equal to 99 .7 megahertz, and resistance R is equal to 12 .0 oom, and induc

An R L C circuit is used in a radio to tune into an FM...

An $R L C$ circuit is used in a radio to tune into an $\mathrm{FM}$ station broadcasting at $f=99.7 \mathrm{MHz}$ . The resistance in the circuit is $R=12.0 \Omega,$ and the inductance is $L=1.40 \mu \mathrm{H}$ . What capacitance should be used?

Key Concepts

Tuning in Radio Circuits

Tuning in radio circuits involves adjusting the reactive components, typically the capacitor in an RLC circuit, to match the circuit’s resonant frequency to the frequency of the desired radio signal. This maximizes the signal pickup by minimizing impedance at that frequency, thereby allowing effective separation of different broadcast frequencies. Understanding this concept is fundamental in the design and operation of radio frequency receivers.

RLC Circuit

An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C) connected in series or parallel. The interplay between these components gives rise to unique dynamic behaviors such as oscillation and damping, which are central to understanding how such circuits respond to alternating current. This concept is crucial in electronics and communication systems, where filtering, tuning, and signal processing are essential.

Resonance Frequency

The resonance frequency in an RLC circuit is the specific frequency at which the inductive and capacitive reactances are equal in magnitude but opposite in phase, effectively canceling each other out. This results in the circuit experiencing a peak in voltage or current response. The resonance frequency is determined by the inductance and capacitance via the relation ? = 1/?(LC), where ? is the angular frequency, and it is critical for designing circuits that selectively filter or tune specific frequencies.

Capacitor Sizing for Resonance

In a resonant RLC circuit, selecting the right capacitance is essential to achieve the desired resonant frequency. By rearranging the resonance condition (f = 1/(2??(LC))), designers can compute the necessary capacitance given a target frequency and a known inductance. This process of capacitor sizing is key in applications like radio receivers, where precise frequency tuning is required.

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