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We = ? ( Critical angular fraguency) ow=? (Bandwidth in angular frapuanıy) ( Transfer function T= V. (w) ) V; (w) T=?

We = ? ( Critical angular fraguency) ow=? (Bandwidth in angular frapuanıy) ( Transfer function T= V. (w) ) V; (w) T=?

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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### Electrical Circuit Analysis #### Problem 3(a) **Circuit Description:** - A source generates the signal: \( \frac{4}{\pi} \sin 10^3 t \). - Components in the circuit: - Inductor: \(2 \, \text{H}\) - Capacitor: \(10^{-6} \, \text{F}\) - Resistor: \(3 \, \Omega\) **Tasks:** 1. **Critical Angular Frequency \( \omega_c = ? \):** Calculate the angular frequency at which the circuit responds most efficiently. 2. **Bandwidth in Angular Frequency \( \Delta \omega = ? \):** Determine the range of frequencies over which the circuit operates effectively. 3. **Transfer Function \( T = ? \):** Find the ratio of the output voltage \( V_o(\omega) \) to the input voltage \( V_i(\omega) \). #### Problem 3(b) **Modified Circuit Description:** - Signal from the source is expressed using the series: \[ \sum_{n=1, \, \text{odd}}^{\infty} \frac{4}{n\pi} \sin(n \times 10^3 t) \] - Circuit components remain the same: - Inductor: \(2 \, \text{H}\) - Capacitor: \(10^{-6} \, \text{F}\) - Resistor: \(3 \, \Omega\) **Objective:** - Calculate the output voltage \( V_o \). #### Note: The diagrams show an LC circuit (Inductor and Capacitor) in series with a resistor, driven by an AC voltage source. Analyze the circuit to derive expressions for the critical points and functions listed above.
Transcribed Image Text:### Electrical Circuit Analysis #### Problem 3(a) **Circuit Description:** - A source generates the signal: \( \frac{4}{\pi} \sin 10^3 t \). - Components in the circuit: - Inductor: \(2 \, \text{H}\) - Capacitor: \(10^{-6} \, \text{F}\) - Resistor: \(3 \, \Omega\) **Tasks:** 1. **Critical Angular Frequency \( \omega_c = ? \):** Calculate the angular frequency at which the circuit responds most efficiently. 2. **Bandwidth in Angular Frequency \( \Delta \omega = ? \):** Determine the range of frequencies over which the circuit operates effectively. 3. **Transfer Function \( T = ? \):** Find the ratio of the output voltage \( V_o(\omega) \) to the input voltage \( V_i(\omega) \). #### Problem 3(b) **Modified Circuit Description:** - Signal from the source is expressed using the series: \[ \sum_{n=1, \, \text{odd}}^{\infty} \frac{4}{n\pi} \sin(n \times 10^3 t) \] - Circuit components remain the same: - Inductor: \(2 \, \text{H}\) - Capacitor: \(10^{-6} \, \text{F}\) - Resistor: \(3 \, \Omega\) **Objective:** - Calculate the output voltage \( V_o \). #### Note: The diagrams show an LC circuit (Inductor and Capacitor) in series with a resistor, driven by an AC voltage source. Analyze the circuit to derive expressions for the critical points and functions listed above.
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