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(a) Show that the system of differential equations for the currents i₂(t) and i3(t) in the electrical network shown in the figure below is diz L1 + Ri₂ + Ri3 = E(t) dt di3 L2 + Ri₂ + Ri3 = E(t). dt Ail 13(t) = E R 1₂ 13 L₁ (c) Determine the current i₁(t). 1₁ (t) = 00000 L₂ By Kirchhoff's first law we have the following relationship between 1₁, 12, and 13. /1 i= 12 +13 By applying Kirchhoff's second law to the 1₁, 12 loop, we obtain the following. E(t) = R 1₁ + ₁ By applying Kirchhoff's second law to the 1₁, 13 loop, we obtain the following. E(t) = R 1₁ + 1₂ Writing in terms of 12 and 13 and rearranging terms, one obtains the given system. (b) Solve the system in part (a) if R = 52, L₁= 0.025 h, L₂ = 0.01 h, E = 200 V, i₂(0) = 0, and i3(0) = 0. i₂(t) = 13'

(a) Show that the system of differential equations for the currents i₂(t) and i3(t) in the electrical network shown in the figure below is diz L1 + Ri₂ + Ri3 = E(t) dt di3 L2 + Ri₂ + Ri3 = E(t). dt Ail 13(t) = E R 1₂ 13 L₁ (c) Determine the current i₁(t). 1₁ (t) = 00000 L₂ By Kirchhoff's first law we have the following relationship between 1₁, 12, and 13. /1 i= 12 +13 By applying Kirchhoff's second law to the 1₁, 12 loop, we obtain the following. E(t) = R 1₁ + ₁ By applying Kirchhoff's second law to the 1₁, 13 loop, we obtain the following. E(t) = R 1₁ + 1₂ Writing in terms of 12 and 13 and rearranging terms, one obtains the given system. (b) Solve the system in part (a) if R = 52, L₁= 0.025 h, L₂ = 0.01 h, E = 200 V, i₂(0) = 0, and i3(0) = 0. i₂(t) = 13'

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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(a) Show that the system of differential equations for the currents i₂(t) and i3(t) in the electrical network shown in the figure below is diz L1 + Ri₂ + Ri3 = E(t) dt di3 L2 + Ri₂ + Ri3 = E(t). dt Ail 13(t) = E R 1₂ 13 L₁ (c) Determine the current i₁(t). 1₁ (t) = 00000 L₂ By Kirchhoff's first law we have the following relationship between 1₁, 12, and 13. /1 i= 12 +13 By applying Kirchhoff's second law to the 1₁, 12 loop, we obtain the following. E(t) = R 1₁ + ₁ By applying Kirchhoff's second law to the 1₁, 13 loop, we obtain the following. E(t) = R 1₁ + 1₂ Writing in terms of 12 and 13 and rearranging terms, one obtains the given system. (b) Solve the system in part (a) if R = 52, L₁= 0.025 h, L₂ = 0.01 h, E = 200 V, i₂(0) = 0, and i3(0) = 0. i₂(t) = 13'
Transcribed Image Text:(a) Show that the system of differential equations for the currents i₂(t) and i3(t) in the electrical network shown in the figure below is diz L1 + Ri₂ + Ri3 = E(t) dt di3 L2 + Ri₂ + Ri3 = E(t). dt Ail 13(t) = E R 1₂ 13 L₁ (c) Determine the current i₁(t). 1₁ (t) = 00000 L₂ By Kirchhoff's first law we have the following relationship between 1₁, 12, and 13. /1 i= 12 +13 By applying Kirchhoff's second law to the 1₁, 12 loop, we obtain the following. E(t) = R 1₁ + ₁ By applying Kirchhoff's second law to the 1₁, 13 loop, we obtain the following. E(t) = R 1₁ + 1₂ Writing in terms of 12 and 13 and rearranging terms, one obtains the given system. (b) Solve the system in part (a) if R = 52, L₁= 0.025 h, L₂ = 0.01 h, E = 200 V, i₂(0) = 0, and i3(0) = 0. i₂(t) = 13'
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