The image contains a problem about analyzing a circuit using a differential equation approach to find the expression for current \( i_L(t) \) for \( t > 0 \). The circuit provided in Figure P7.14 comprises the following components:- A 6V voltage source- Resistors with values: 12Ω, 6Ω, 6Ω, and 3Ω- An inductor with a value of 1H- A switch, which is closed at \( t = 0 \)The task is to select the correct plot of \( i_L(t) \) from the given options.**Graphs Explanation:**1. **Graph 1:** - The plot starts at a value of approximately 0.89 at \( t = 0 \). - The current decreases exponentially and stabilizes as it approaches zero. - The curve looks like a classic exponential decay.2. **Graph 2:** - The plot starts at a value of 0.667 at \( t = 0 \). - The current decreases exponentially and levels off, trending toward zero. - Features a smooth decay characteristic, typical of an RL circuit.3. **Graph 3:** - The plot starts at a value of 6.67 at \( t = 0 \). - It shows an exponential decay that also stabilizes towards zero. - This curve represents a steeper initial decrease compared to the others.4. **Graph 4:** - The initial value is at 0.7273 at \( t = 0 \). - It shows an exponential decay pattern similar to the other plots. - The transition to zero current is also smooth, without fluctuations.Each graph represents potential solutions for \( i_L(t) \) based on differential equations for the RL circuit. The goal is to identify which graph correctly models the circuit’s behavior after the switch is closed at \( t = 0 \).

Answered: Image /qna-images/answer/81ba22a2-d14f-4575-b4c4-c49fffb7086d.jpg

Use the differential equation approach to find i(t) for t>0 in the circuit in Fig. P7.14. Select the correct plot for it (t). O 3120 Figure P7.14 -06 04 02 (0.0.89) (0.0.667) (0, 6.67) 06 -04 -02 3602 Ո -0.5- 0 0 (0,0.7273) 02 6V 04 06 04 1=0 05 0.5 3602 06 1H m (1) 08 302 12 14

Use the differential equation approach to find i(t) for t>0 in the circuit in Fig. P7.14. Select the correct plot for it (t). O 3120 Figure P7.14 -06 04 02 (0.0.89) (0.0.667) (0, 6.67) 06 -04 -02 3602 Ո -0.5- 0 0 (0,0.7273) 02 6V 04 06 04 1=0 05 0.5 3602 06 1H m (1) 08 302 12 14

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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Question

The image contains a problem about analyzing a circuit using a differential equation approach to find the expression for current \( i_L(t) \) for \( t > 0 \). The circuit provided in Figure P7.14 comprises the following components:

- A 6V voltage source
- Resistors with values: 12Ω, 6Ω, 6Ω, and 3Ω
- An inductor with a value of 1H
- A switch, which is closed at \( t = 0 \)

The task is to select the correct plot of \( i_L(t) \) from the given options.

**Graphs Explanation:**

1. **Graph 1:**
- The plot starts at a value of approximately 0.89 at \( t = 0 \).
- The current decreases exponentially and stabilizes as it approaches zero.
- The curve looks like a classic exponential decay.

2. **Graph 2:**
- The plot starts at a value of 0.667 at \( t = 0 \).
- The current decreases exponentially and levels off, trending toward zero.
- Features a smooth decay characteristic, typical of an RL circuit.

3. **Graph 3:**
- The plot starts at a value of 6.67 at \( t = 0 \).
- It shows an exponential decay that also stabilizes towards zero.
- This curve represents a steeper initial decrease compared to the others.

4. **Graph 4:**
- The initial value is at 0.7273 at \( t = 0 \).
- It shows an exponential decay pattern similar to the other plots.
- The transition to zero current is also smooth, without fluctuations.

Each graph represents potential solutions for \( i_L(t) \) based on differential equations for the RL circuit. The goal is to identify which graph correctly models the circuit’s behavior after the switch is closed at \( t = 0 \).

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