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4. Find the instantaneous power p(t) dissipated by the circuit for t > 1 second. 5. Find the total energy dissipated bey the resistors during this time. 6. Find the total energy stored in the capacitor. 1 ΚΩ 10 V + 6 ΚΩ 2 ΚΩ 2/3 u F

4. Find the instantaneous power p(t) dissipated by the circuit for t > 1 second. 5. Find the total energy dissipated bey the resistors during this time. 6. Find the total energy stored in the capacitor. 1 ΚΩ 10 V + 6 ΚΩ 2 ΚΩ 2/3 u F

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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**Circuit Analysis Problem** Consider a circuit where, at time \( t = 0 \), the switch is closed after being open for a long time. You need to solve the following questions based on the given conditions: 1. **Find \( v(t) \):** Determine the voltage across the capacitor for \( t > 0 \). At time \( t = 1 \) second, the switch opens. 2. **Voltage at \( t = 1 \) second:** What is \( v(t) \) at \( t = 1 \) second, just before the switch opens? 3. **Decay Time Calculation:** Determine the time it takes for \( v(t) \) to reach \( \frac{1}{3} \times v(t = 1 \text{ sec}) \). 4. **Instantaneous Power \( p(t) \):** Calculate the instantaneous power dissipated by the circuit for \( t > 1 \) second. 5. **Total Energy Dissipated:** Find the total energy dissipated by the resistors during this time. 6. **Energy Stored in Capacitor:** Calculate the total energy stored in the capacitor. **Circuit Diagram Explanation:** - The circuit contains a 10 V battery connected to a 1 kΩ resistor. - This is in series with a parallel combination of a 6 kΩ resistor, a 2 kΩ resistor, and a \( \frac{2}{3} \) microfarad capacitor. - Initially, the circuit is analyzed with the switch closed and then with the switch open at \( t = 1 \) second.
Transcribed Image Text:**Circuit Analysis Problem** Consider a circuit where, at time \( t = 0 \), the switch is closed after being open for a long time. You need to solve the following questions based on the given conditions: 1. **Find \( v(t) \):** Determine the voltage across the capacitor for \( t > 0 \). At time \( t = 1 \) second, the switch opens. 2. **Voltage at \( t = 1 \) second:** What is \( v(t) \) at \( t = 1 \) second, just before the switch opens? 3. **Decay Time Calculation:** Determine the time it takes for \( v(t) \) to reach \( \frac{1}{3} \times v(t = 1 \text{ sec}) \). 4. **Instantaneous Power \( p(t) \):** Calculate the instantaneous power dissipated by the circuit for \( t > 1 \) second. 5. **Total Energy Dissipated:** Find the total energy dissipated by the resistors during this time. 6. **Energy Stored in Capacitor:** Calculate the total energy stored in the capacitor. **Circuit Diagram Explanation:** - The circuit contains a 10 V battery connected to a 1 kΩ resistor. - This is in series with a parallel combination of a 6 kΩ resistor, a 2 kΩ resistor, and a \( \frac{2}{3} \) microfarad capacitor. - Initially, the circuit is analyzed with the switch closed and then with the switch open at \( t = 1 \) second.
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