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Name a) Given v,(t) = 50 cos(1200t) V, use voltage divider to calculate the voltage v in Circuit 5a. Answer in the time domain. 10 Ω 5 mF + v ! 20 mH Circuit 5a

Name a) Given v,(t) = 50 cos(1200t) V, use voltage divider to calculate the voltage v in Circuit 5a. Answer in the time domain. 10 Ω 5 mF + v ! 20 mH Circuit 5a

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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**Transcription for Educational Website:** **Problem Statement:** a) Given \( v_s(t) = 50 \cos(1200t) \, \text{V} \), use voltage divider to calculate the voltage \( v \) in Circuit 5a. Answer in the time domain. **Circuit Description:** This is an RLC series circuit labeled as "Circuit 5a." It includes the following components arranged in a loop: - A voltage source, \( v_s \), providing the input voltage \( 50 \cos(1200t) \) volts. - A resistor (\( 10 \, \Omega \)) is connected in series with the voltage source. - A capacitor (\( 5 \, \text{mF} \)) is connected next in the series. - An inductor (\( 20 \, \text{mH} \)) completes the series circuit. The current flows from the voltage source through the resistor, capacitor, and inductor, returning back to the voltage source. The voltage across the capacitor and the inductor is labeled as \( v \). **Objective:** To calculate the voltage \( v \) across the capacitor and inductor using a voltage divider rule in the time domain. (Note: Additional mathematical operations may be necessary to apply the voltage divider rule considering the impedance of the capacitor and inductor at the given frequency.)
Transcribed Image Text:**Transcription for Educational Website:** **Problem Statement:** a) Given \( v_s(t) = 50 \cos(1200t) \, \text{V} \), use voltage divider to calculate the voltage \( v \) in Circuit 5a. Answer in the time domain. **Circuit Description:** This is an RLC series circuit labeled as "Circuit 5a." It includes the following components arranged in a loop: - A voltage source, \( v_s \), providing the input voltage \( 50 \cos(1200t) \) volts. - A resistor (\( 10 \, \Omega \)) is connected in series with the voltage source. - A capacitor (\( 5 \, \text{mF} \)) is connected next in the series. - An inductor (\( 20 \, \text{mH} \)) completes the series circuit. The current flows from the voltage source through the resistor, capacitor, and inductor, returning back to the voltage source. The voltage across the capacitor and the inductor is labeled as \( v \). **Objective:** To calculate the voltage \( v \) across the capacitor and inductor using a voltage divider rule in the time domain. (Note: Additional mathematical operations may be necessary to apply the voltage divider rule considering the impedance of the capacitor and inductor at the given frequency.)
Expert Solution
Step 1

For the given circuit

w=1200 rad/s

R= 10 ohms

XL = jwL = j24 ohms

Xc = -j/wc = -j0.167 ohms

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