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6.4-5 Determine the voltage v(t) in the circuit of Fig. P6.3-5.

6.4-5 Determine the voltage v(t) in the circuit of Fig. P6.3-5.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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6.4-5 Determine the voltage v(t) in the circuit of Fig. P6.3-5.
**Text Transcription:** ### Exercise 6.3-5 **Problem Statement:** Draw the phasor circuit for the circuit of Fig. P6.3-5. **Figure P6.3-5:** This figure shows an electrical circuit with the following components: - **Voltage Source:** A sinusoidal voltage source given as \(5 \cos 2t \, \text{V}\). - **Inductor:** A 3 Henry (H) inductor. - **Resistor:** A 3 Ohm (Ω) resistor. - **Capacitor:** A capacitor of \( \frac{1}{6} \) Farad (F). The circuit has a loop with the voltage source placed in series with the inductor, the resistor, and the capacitor. The circuit is oriented in a clockwise direction. The voltage across the capacitor is labeled as \(v(t)\), with the positive side at the top and the negative side at the bottom. The configuration is typical for analyzing steady-state sinusoidal signals using phasors. **Explanation for Phasor Circuit:** When drawing a phasor circuit, the sinusoidal sources and reactive components (inductors and capacitors) need to be converted into their phasor equivalents. The inductor and capacitor will be replaced by their respective impedances: - Inductive impedance is \( j\omega L \). - Capacitive impedance is \( \frac{1}{j\omega C} \). where \(\omega\) is the angular frequency of the source, L is the inductance, and C is the capacitance. Analyze the circuit using these phasor relationships to better understand its behavior in the frequency domain.
Transcribed Image Text:**Text Transcription:** ### Exercise 6.3-5 **Problem Statement:** Draw the phasor circuit for the circuit of Fig. P6.3-5. **Figure P6.3-5:** This figure shows an electrical circuit with the following components: - **Voltage Source:** A sinusoidal voltage source given as \(5 \cos 2t \, \text{V}\). - **Inductor:** A 3 Henry (H) inductor. - **Resistor:** A 3 Ohm (Ω) resistor. - **Capacitor:** A capacitor of \( \frac{1}{6} \) Farad (F). The circuit has a loop with the voltage source placed in series with the inductor, the resistor, and the capacitor. The circuit is oriented in a clockwise direction. The voltage across the capacitor is labeled as \(v(t)\), with the positive side at the top and the negative side at the bottom. The configuration is typical for analyzing steady-state sinusoidal signals using phasors. **Explanation for Phasor Circuit:** When drawing a phasor circuit, the sinusoidal sources and reactive components (inductors and capacitors) need to be converted into their phasor equivalents. The inductor and capacitor will be replaced by their respective impedances: - Inductive impedance is \( j\omega L \). - Capacitive impedance is \( \frac{1}{j\omega C} \). where \(\omega\) is the angular frequency of the source, L is the inductance, and C is the capacitance. Analyze the circuit using these phasor relationships to better understand its behavior in the frequency domain.
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