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At time t = : 0 the switch is closed after being open for a long time. 1. Find v(t) across the capacitor for t > 0. At time t= 1 second, the switch opens. 2. What is v(t) at t = 1 second, right before the switch opens? 3. Determine the time it takes for v(t) = 1/3 × v(t = 1 sec).

At time t = : 0 the switch is closed after being open for a long time. 1. Find v(t) across the capacitor for t > 0. At time t= 1 second, the switch opens. 2. What is v(t) at t = 1 second, right before the switch opens? 3. Determine the time it takes for v(t) = 1/3 × v(t = 1 sec).

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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**Problem Description:** At time \( t = 0 \), the switch is closed after being open for a long time. 1. Find \( v(t) \) across the capacitor for \( t > 0 \). At time \( t = 1 \) second, the switch opens. 2. What is \( v(t) \) at \( t = 1 \) second, right before the switch opens? 3. Determine the time it takes for \( v(t) = \frac{1}{3} \times v(t = 1 \text{ sec}) \). 4. Find the instantaneous power \( p(t) \) dissipated by the circuit for \( t > 1 \) second. 5. Find the total energy dissipated by the resistors during this time. 6. Find the total energy stored in the capacitor. **Circuit Diagram:** - The circuit consists of a 10 V voltage source connected in series with a switch. - After the switch, there is a 1 kΩ resistor, followed by a parallel combination of a 6 kΩ resistor, a 2 kΩ resistor, and a 2/3 μF capacitor. **Explanation of Components:** - **Voltage Source (10 V):** Provides a constant voltage to the circuit. - **Switch:** Controls the connection of the circuit, initially closed and then opened at \( t = 1 \) second. - **Resistors (1 kΩ, 6 kΩ, 2 kΩ):** These resistors limit current and dissipate power as heat. - **Capacitor (2/3 μF):** Stores energy in an electric field, with a capacitance of 2/3 microfarads.
Transcribed Image Text:**Problem Description:** At time \( t = 0 \), the switch is closed after being open for a long time. 1. Find \( v(t) \) across the capacitor for \( t > 0 \). At time \( t = 1 \) second, the switch opens. 2. What is \( v(t) \) at \( t = 1 \) second, right before the switch opens? 3. Determine the time it takes for \( v(t) = \frac{1}{3} \times v(t = 1 \text{ sec}) \). 4. Find the instantaneous power \( p(t) \) dissipated by the circuit for \( t > 1 \) second. 5. Find the total energy dissipated by the resistors during this time. 6. Find the total energy stored in the capacitor. **Circuit Diagram:** - The circuit consists of a 10 V voltage source connected in series with a switch. - After the switch, there is a 1 kΩ resistor, followed by a parallel combination of a 6 kΩ resistor, a 2 kΩ resistor, and a 2/3 μF capacitor. **Explanation of Components:** - **Voltage Source (10 V):** Provides a constant voltage to the circuit. - **Switch:** Controls the connection of the circuit, initially closed and then opened at \( t = 1 \) second. - **Resistors (1 kΩ, 6 kΩ, 2 kΩ):** These resistors limit current and dissipate power as heat. - **Capacitor (2/3 μF):** Stores energy in an electric field, with a capacitance of 2/3 microfarads.
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