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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)
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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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 \( t = 0 \).
Transcribed Image Text: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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