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Ch 32: AC Circuits
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 32: AC CircuitsProblema 32a
Capitolo 32, Problema 32a

For the circuit of FIGURE EX32.32, What is the resonance frequency, in both rad/s and Hz?

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1
Step 1: Identify the components in the circuit. The circuit consists of a resistor (R = 10 Ω), an inductor (L = 10 mH), and a capacitor (C = 10 μF) connected in series with an AC voltage source.
Step 2: Recall the formula for resonance frequency in a series RLC circuit. The resonance frequency occurs when the inductive reactance and capacitive reactance cancel each other out. The formula for angular resonance frequency (ω₀) is: ω₀ = 1 / √(L * C).
Step 3: Substitute the given values into the formula for angular resonance frequency. Use L = 10 mH = 10 × 10⁻³ H and C = 10 μF = 10 × 10⁻⁶ F. The formula becomes: ω₀ = 1 / √((10 × 10⁻³) * (10 × 10⁻⁶)).
Step 4: Convert the angular resonance frequency (ω₀) to the resonance frequency in Hz (f₀). The relationship between angular frequency and frequency is: f₀ = ω₀ / (2π).
Step 5: After calculating ω₀ and f₀, you will have the resonance frequency in both rad/s and Hz. Ensure units are consistent throughout the calculation.

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Resonance Frequency

Resonance frequency is the frequency at which a system naturally oscillates with maximum amplitude. In electrical circuits, it occurs when the inductive reactance equals the capacitive reactance, leading to a condition where the impedance is minimized. This frequency can be calculated using the formula f₀ = 1 / (2π√(LC)), where L is inductance and C is capacitance.
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Resonance in Series LRC Circuits

Inductive Reactance

Inductive reactance (X_L) is the opposition that an inductor presents to alternating current (AC) due to its inductance. It is calculated using the formula X_L = ωL, where ω is the angular frequency in rad/s and L is the inductance in henries. This concept is crucial for determining the behavior of circuits at different frequencies, especially in resonance conditions.
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Mutual Induction

Capacitive Reactance

Capacitive reactance (X_C) is the opposition that a capacitor presents to AC, which decreases with increasing frequency. It is given by the formula X_C = 1 / (ωC), where C is the capacitance in farads. Understanding capacitive reactance is essential for analyzing how capacitors interact with inductors in resonant circuits, affecting the overall impedance and resonance frequency.
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Capacitors & Capacitance (Intro)
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