(a) An inductor designed to filter high-frequency noise from...

(a) An inductor designed to filter high-frequency noise from power supplied to a personal computer is placed in series with the computer. What minimum inductance should it have to produce a 2.00 $\mathrm{k} \Omega$ reactance for 15.0 $\mathrm{kHz}$ noise? (b) What is its reactance at 60.0 $\mathrm{Hz}$ ?

Key Concepts

Series Circuit Analysis

In series circuit analysis, components are connected end-to-end, and the same current flows through each component. When an inductor is placed in series with a load, its reactance influences the overall impedance of the circuit. This principle is used to tailor the circuit’s response to different frequencies, essential for achieving desired filtering characteristics.

Inductive Reactance

Inductive reactance is the measure of an inductor's opposition to a change in current in an AC circuit, and it is frequency-dependent. It is calculated using the formula X? = 2?fL, where f is the frequency and L is the inductance. This concept is pivotal in designing circuits that either block or pass certain frequencies, making it crucial in filtering applications.

Angular Frequency

Angular frequency, represented by ?, is related to the cyclic frequency by the relation ? = 2?f. It provides a convenient measure for the oscillatory behavior of AC signals and is integral in the formulas used to compute reactive components in AC circuits, such as inductive reactance.

Passive Filtering

Passive filtering involves using circuit elements like resistors, capacitors, and inductors to allow or block specific frequency components of a signal without the need for external power. The use of an inductor to filter high-frequency noise in a circuit exemplifies passive filtering, as the inductor offers substantial reactance at high frequencies, thereby reducing the unwanted noise.

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