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(Please answer to the fourth decimal place - i.e 14.3225)

(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.
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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