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2-6 - Create assignment 00224 Homework 6 Mar 03 at 6:08 pm...

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Create assignment, 00224, Homework 6, Mar 03 at 6:08 pm 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. Current in a Two Loop Circuit 28:06, trigonometry, numeric, > 1 min, nor- mal. 001 8 V 1 . 1 V 3 . 1 V I 1 1 . 1 Ω 2 . 2 Ω I 2 4 . 3 Ω I 3 8 . 4 Ω Find the current I 1 in the 1 . 1 Ω resistor at the bottom of the circuit between the two power supplies. Correct answer: 1 . 14738 A. Explanation: E 1 E 2 E 3 I 1 R A R B I 2 R C I 3 R D At a junction (Conservation of Charge) I 1 + I 2 - I 3 = 0 . (1) Kirchhoff’s law on the large outside loop gives ( R A + R B ) I 1 + R D I 3 = E 1 + E 2 . (2) Kirchhoff’s law on the right-hand small loop gives R C I 2 + R D I 3 = E 3 . (3) Let : R A = 1 . 1 Ω , R B = 2 . 2 Ω , R C = 4 . 3 Ω , R D = 8 . 4 Ω , E 1 = 8 V , E 2 = 1 . 1 V , and E 3 = 3 . 1 V . Using determinants, I 1 = fl fl fl fl fl fl 0 1 - 1 E 1 + E 2 0 R D E 3 R C R D fl fl fl fl fl fl fl fl fl fl fl fl 1 1 - 1 R A + R B 0 R D 0 R C R D fl fl fl fl fl fl Expanding along the first row, the numera- tor is D 1 = fl fl fl fl fl fl 0 1 - 1 E 1
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