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Ch. 30 - Inductance, Electromagnetic Oscillations, and AC Circuits
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 30 - Inductance, Electromagnetic Oscillations, and AC CircuitsProblema 43
Capitolo 29, Problema 43

A 10.0-k Ω resistor is in series with a 34.0-mH inductor and an ac source. Calculate the impedance of the circuit if the source frequency is (a) 55.0 Hz; (b) 55.0 kHz.

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Determine the formula for the impedance of an R-L series circuit. The total impedance \( Z \) is given by \( Z = \sqrt{R^2 + (X_L)^2} \), where \( R \) is the resistance and \( X_L \) is the inductive reactance.
Calculate the inductive reactance \( X_L \) using the formula \( X_L = 2 \pi f L \), where \( f \) is the frequency of the source and \( L \) is the inductance of the inductor. Perform this calculation for both \( f = 55.0 \ \text{Hz} \) and \( f = 55.0 \ \text{kHz} \).
Substitute the given values for \( R = 10.0 \ \text{k}\Omega = 10,000 \ \Omega \), \( L = 34.0 \ \text{mH} = 0.034 \ \text{H} \), and the calculated \( X_L \) for each frequency into the impedance formula \( Z = \sqrt{R^2 + (X_L)^2} \).
For part (a), use the calculated \( X_L \) at \( f = 55.0 \ \text{Hz} \) to find the impedance \( Z \).
For part (b), use the calculated \( X_L \) at \( f = 55.0 \ \text{kHz} \) to find the impedance \( Z \).

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Impedance in AC Circuits

Impedance (Z) is the total opposition that a circuit offers to the flow of alternating current (AC) and is a combination of resistance (R) and reactance (X). It is expressed as Z = √(R² + X²), where R is the resistance and X is the reactance due to inductors or capacitors. Understanding impedance is crucial for analyzing AC circuits, as it affects the current and voltage relationship.
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Impedance in AC Circuits

Inductive Reactance

Inductive reactance (X_L) is the opposition to the change in current flow through an inductor in an AC circuit, calculated using the formula X_L = 2πfL, where f is the frequency and L is the inductance. This concept is essential for determining how inductors behave at different frequencies, impacting the overall impedance of the circuit.
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Mutual Induction

Series Circuit Behavior

In a series circuit, components are connected end-to-end, and the same current flows through each component. The total impedance is the sum of the individual resistances and reactances. This behavior is important for calculating the overall impedance in circuits with resistors and inductors, as it influences the voltage drop across each component and the total current in the circuit.
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LRC Circuits in Series
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