Consider the RL circuit below. All the resistors have size 6 k 2, the inductor has size 5 mH, and the battery has size 46 V. The switch has been in the right position for a long time. Att = 0, it is flipped into the left position. Calculate the energy stored in the inductor at t = 1.6 us, in units of pJ. (1 pJ = 1012 J) R3 S1 R1 R2 L1 V1+

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

**RL Circuit Analysis and Energy Calculation in an Inductor**

### Problem Statement

Consider the RL circuit shown below. 

- All resistors (R1, R2, and R3) have a resistance of 6 kΩ.
- The inductor (L1) has an inductance of 5 mH.
- The battery (V1) has a voltage of 46 V.

The switch (S1) has been in the right position for a long time. At time \( t = 0 \), the switch is flipped to the left position.

Calculate the energy stored in the inductor at \( t = 1.6 \ \mu s \) in units of picojoules (pJ). (1 pJ \( = 10^{-12} \) Joules)

### Circuit Diagram Explanation

- **Resistive Network**:
  - The circuit consists of three resistors, R1, R2, and R3, each with a resistance of 6 kΩ.
- **Inductor and Switch**:
  - An inductor, L1 with an inductance of 5 mH, is connected in series with a switch (S1).
- **Voltage Source**:
  - The voltage source V1 supplies a constant voltage of 46 V.

**Initial Condition**:
- Initially, the switch S1 is in the right position, allowing the circuit involving R3 and the voltage source V1 to be active for a long duration, thus establishing a steady-state.

**At \( t = 0 \)**:
- The switch is flipped to the left position, involving the resistors R1, R2, and the inductor L1 in the circuit.

### Task

Calculate the energy stored in the inductor at \( t = 1.6 \ \mu s \).

### Relevant Equations

1. **Energy Stored in the Inductor**:
\[ E = \frac{1}{2} L I^2 \]
where \( I \) is the current through the inductor at time \( t \).

2. **Current through the Inductor in an RL Circuit**:
\[ I(t) = I_0 e^{-\frac{R}{L} t} \]
where:
  - \( I_0 \) is the initial current through the inductor.
  - \( R \) is the equivalent resistance in the circuit.
  - \( L \) is
Transcribed Image Text:**RL Circuit Analysis and Energy Calculation in an Inductor** ### Problem Statement Consider the RL circuit shown below. - All resistors (R1, R2, and R3) have a resistance of 6 kΩ. - The inductor (L1) has an inductance of 5 mH. - The battery (V1) has a voltage of 46 V. The switch (S1) has been in the right position for a long time. At time \( t = 0 \), the switch is flipped to the left position. Calculate the energy stored in the inductor at \( t = 1.6 \ \mu s \) in units of picojoules (pJ). (1 pJ \( = 10^{-12} \) Joules) ### Circuit Diagram Explanation - **Resistive Network**: - The circuit consists of three resistors, R1, R2, and R3, each with a resistance of 6 kΩ. - **Inductor and Switch**: - An inductor, L1 with an inductance of 5 mH, is connected in series with a switch (S1). - **Voltage Source**: - The voltage source V1 supplies a constant voltage of 46 V. **Initial Condition**: - Initially, the switch S1 is in the right position, allowing the circuit involving R3 and the voltage source V1 to be active for a long duration, thus establishing a steady-state. **At \( t = 0 \)**: - The switch is flipped to the left position, involving the resistors R1, R2, and the inductor L1 in the circuit. ### Task Calculate the energy stored in the inductor at \( t = 1.6 \ \mu s \). ### Relevant Equations 1. **Energy Stored in the Inductor**: \[ E = \frac{1}{2} L I^2 \] where \( I \) is the current through the inductor at time \( t \). 2. **Current through the Inductor in an RL Circuit**: \[ I(t) = I_0 e^{-\frac{R}{L} t} \] where: - \( I_0 \) is the initial current through the inductor. - \( R \) is the equivalent resistance in the circuit. - \( L \) is
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