In the circuit below, the switch is closed at time t = 0 after being open for a long time. 1. Find v(t) for 0 < t. What is the RC time constant? At time t = 1 second, the switch is suddenly opened. 2. Find v(t) at t = 1 second right before the switch opens. [hint: a capacitor acts as an open circuit when it's in its steady state]. 3. Determine the time it takes the capacitor voltage to decay to 1/3 of its initial value.
In the circuit below, the switch is closed at time t = 0 after being open for a long time. 1. Find v(t) for 0 < t. What is the RC time constant? At time t = 1 second, the switch is suddenly opened. 2. Find v(t) at t = 1 second right before the switch opens. [hint: a capacitor acts as an open circuit when it's in its steady state]. 3. Determine the time it takes the capacitor voltage to decay to 1/3 of its initial value.
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![### Problem Statement
In the circuit below, the switch is closed at time \( t = 0 \) after being open for a long time.
1. Find \( v(t) \) for \( 0 < t \). What is the RC time constant?
At time \( t = 1 \) second, the switch is suddenly opened.
2. Find \( v(t) \) at \( t = 1 \) second right before the switch opens. [Hint: a capacitor acts as an open circuit when it’s in its steady state].
3. Determine the time it takes the capacitor voltage to decay to \( \frac{1}{3} \) of its initial value.
4. Find the instantaneous power dissipated by the circuit for all \( t > 1 \) second, as well as the total energy dissipated for all \( t > 1 \) second.
### Circuit Description
The circuit consists of:
- A voltage source of 11 V.
- A switch that controls the connection.
- A 1 kΩ resistor in series.
- A parallel combination of a 10 kΩ resistor and a 100 μF capacitor, connecting at the point where \( v(t) \) is measured.
### Diagram Explanation
The circuit diagram shows a simple RC series circuit with the following characteristics:
- The voltage source is connected to a 1 kΩ resistor, which then connects to a parallel combination of a 10 kΩ resistor and a 100 μF capacitor.
- The 11 V supply voltage feeds directly into these components.
- The switch controls the starting point of the circuit action described in the problem.
This setup is typical for analyzing transient response in RC circuits and involves solving for voltages and dissipated power over time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F099a9854-7cc3-46b9-a37c-ec0486b4a12a%2Fc288b59e-7a51-4dce-bf79-ae13c4dbed32%2Fakni73j_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
In the circuit below, the switch is closed at time \( t = 0 \) after being open for a long time.
1. Find \( v(t) \) for \( 0 < t \). What is the RC time constant?
At time \( t = 1 \) second, the switch is suddenly opened.
2. Find \( v(t) \) at \( t = 1 \) second right before the switch opens. [Hint: a capacitor acts as an open circuit when it’s in its steady state].
3. Determine the time it takes the capacitor voltage to decay to \( \frac{1}{3} \) of its initial value.
4. Find the instantaneous power dissipated by the circuit for all \( t > 1 \) second, as well as the total energy dissipated for all \( t > 1 \) second.
### Circuit Description
The circuit consists of:
- A voltage source of 11 V.
- A switch that controls the connection.
- A 1 kΩ resistor in series.
- A parallel combination of a 10 kΩ resistor and a 100 μF capacitor, connecting at the point where \( v(t) \) is measured.
### Diagram Explanation
The circuit diagram shows a simple RC series circuit with the following characteristics:
- The voltage source is connected to a 1 kΩ resistor, which then connects to a parallel combination of a 10 kΩ resistor and a 100 μF capacitor.
- The 11 V supply voltage feeds directly into these components.
- The switch controls the starting point of the circuit action described in the problem.
This setup is typical for analyzing transient response in RC circuits and involves solving for voltages and dissipated power over time.
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