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The two parallel inductors in the figure below are connected across the terminals of a black box at t = 0. The resulting voltage v for t> 0 is known to be 12e-V. It is also known that ₁ (0) = 2A and i2(0) = 4A. i1(t) L1 3 H i2(t) L2 6 H i(t) t=0 Black Box (a) Replace the original inductors with an euivalent inductor and find i(t) for t≥ 0. (b) Find i₁(t) for t≥ 0. (c) Find i₂(t) for t ≥ 0.

The two parallel inductors in the figure below are connected across the terminals of a black box at t = 0. The resulting voltage v for t> 0 is known to be 12e-V. It is also known that ₁ (0) = 2A and i2(0) = 4A. i1(t) L1 3 H i2(t) L2 6 H i(t) t=0 Black Box (a) Replace the original inductors with an euivalent inductor and find i(t) for t≥ 0. (b) Find i₁(t) for t≥ 0. (c) Find i₂(t) for t ≥ 0.

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 two parallel inductors in the figure below are connected across the terminals of a black box at \( t = 0 \). The resulting voltage \( v \) for \( t > 0 \) is known to be \( 12e^{-t} V \). It is also known that \( i_1(0) = 2A \) and \( i_2(0) = 4A \). **Diagram Explanation:** The diagram shows a circuit with two inductors in parallel. Inductor \( L1 \) has an inductance of 3 henries (H) and inductor \( L2 \) has an inductance of 6 henries (H). The current through \( L1 \) is \( i_1(t) \), and the current through \( L2 \) is \( i_2(t) \). The total current entering the black box is \( i(t) \), and the switch is closed at \( t = 0 \). The black box has a specified voltage across its terminals. **Questions:** (a) Replace the original inductors with an equivalent inductor and find \( i(t) \) for \( t \geq 0 \). (b) Find \( i_1(t) \) for \( t \geq 0 \). (c) Find \( i_2(t) \) for \( t \geq 0 \). (d) How much energy is delivered to the black box in the time interval \( 0 \leq t \leq \infty \). (e) How much energy was initially stored in the parallel inductors? (f) How much energy is trapped in the ideal inductors? (g) Show that your solutions for \( i_1(t) \) and \( i_2(t) \) agree with your answer in (f).
Transcribed Image Text:The two parallel inductors in the figure below are connected across the terminals of a black box at \( t = 0 \). The resulting voltage \( v \) for \( t > 0 \) is known to be \( 12e^{-t} V \). It is also known that \( i_1(0) = 2A \) and \( i_2(0) = 4A \). **Diagram Explanation:** The diagram shows a circuit with two inductors in parallel. Inductor \( L1 \) has an inductance of 3 henries (H) and inductor \( L2 \) has an inductance of 6 henries (H). The current through \( L1 \) is \( i_1(t) \), and the current through \( L2 \) is \( i_2(t) \). The total current entering the black box is \( i(t) \), and the switch is closed at \( t = 0 \). The black box has a specified voltage across its terminals. **Questions:** (a) Replace the original inductors with an equivalent inductor and find \( i(t) \) for \( t \geq 0 \). (b) Find \( i_1(t) \) for \( t \geq 0 \). (c) Find \( i_2(t) \) for \( t \geq 0 \). (d) How much energy is delivered to the black box in the time interval \( 0 \leq t \leq \infty \). (e) How much energy was initially stored in the parallel inductors? (f) How much energy is trapped in the ideal inductors? (g) Show that your solutions for \( i_1(t) \) and \( i_2(t) \) agree with your answer in (f).
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