(Please answer to the fourth decimal place - i.e 14.3225)
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(Please answer to the fourth decimal place - i.e 14.3225)
![## RL Circuit Example
Consider the RL circuit layout illustrated below. Key components and their values are:
- Both resistors, R1 and R2, have a resistance of 8 kΩ.
- The inductor, L1, has an inductance of 69 μH.
- The battery, V1, supplies a voltage of 92 V.
### Initial Conditions
- **Switch Position:** The switch, S1, has been in the right position for an extended time (steady state).
### Event
- **Switch Transition:** At \( t = 0 \), the switch S1 is moved to the left position.
### Calculation Task
Calculate the magnitude of the voltage across the inductor, L1, at \( t = 2.6 \) ns.
### Circuit Diagram Description
The schematic diagram of the described RL circuit is as follows:
- The circuit features two resistors (R1 and R2), one inductor (L1), and one switch (S1).
- R1 is placed directly in the main loop with the battery supply V1.
- S1 is a double-throw switch which connects to R2 and L1 based on its position.
- When S1 is in the right position, R2 is in the circuit; when switched to the left, it bypasses R2, placing L1 directly in the circuit path with R1.
### Diagram
>| Diagram is not visible here |
>|:----------------------------|
* **V1:** Voltage source, 92 V
* **R1:** Resistor, 8 kΩ
* **R2:** Resistor, 8 kΩ
* **L1:** Inductor, 69 μH
* **S1:** Switch
### Analysis
In the initial steady state (when S1 is in the right position for a long time), the inductor behaves as a short circuit. When the switch is flipped at \(t = 0\), the transient response must be analyzed to determine the voltage across the inductor at \(t = 2.6 \) ns.
[Here you would include the calculations and relevant theoretical background for the transient analysis, which are not depicted in this transcription.]
This example demonstrates the dynamic behavior of RL circuits and how they respond to sudden changes in switching states.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F021aca7b-3c6d-4d3c-bfc7-736350e47cc8%2Fb44f5cc4-81e6-4d7f-9a9c-8c9a0597f7c5%2Fpryw21m_processed.png&w=3840&q=75)
Transcribed Image Text:## RL Circuit Example
Consider the RL circuit layout illustrated below. Key components and their values are:
- Both resistors, R1 and R2, have a resistance of 8 kΩ.
- The inductor, L1, has an inductance of 69 μH.
- The battery, V1, supplies a voltage of 92 V.
### Initial Conditions
- **Switch Position:** The switch, S1, has been in the right position for an extended time (steady state).
### Event
- **Switch Transition:** At \( t = 0 \), the switch S1 is moved to the left position.
### Calculation Task
Calculate the magnitude of the voltage across the inductor, L1, at \( t = 2.6 \) ns.
### Circuit Diagram Description
The schematic diagram of the described RL circuit is as follows:
- The circuit features two resistors (R1 and R2), one inductor (L1), and one switch (S1).
- R1 is placed directly in the main loop with the battery supply V1.
- S1 is a double-throw switch which connects to R2 and L1 based on its position.
- When S1 is in the right position, R2 is in the circuit; when switched to the left, it bypasses R2, placing L1 directly in the circuit path with R1.
### Diagram
>| Diagram is not visible here |
>|:----------------------------|
* **V1:** Voltage source, 92 V
* **R1:** Resistor, 8 kΩ
* **R2:** Resistor, 8 kΩ
* **L1:** Inductor, 69 μH
* **S1:** Switch
### Analysis
In the initial steady state (when S1 is in the right position for a long time), the inductor behaves as a short circuit. When the switch is flipped at \(t = 0\), the transient response must be analyzed to determine the voltage across the inductor at \(t = 2.6 \) ns.
[Here you would include the calculations and relevant theoretical background for the transient analysis, which are not depicted in this transcription.]
This example demonstrates the dynamic behavior of RL circuits and how they respond to sudden changes in switching states.
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