Question

Calculate current through individual resistors in the following circuit diagram. Please show ALL work.

3 Α 2 Ω νη 8 Ω ν2 4 Ω νη 8Ω 5 A Μν 4 Ω AM 2 Ω 12V

Answer 1

BA Giveni thirty Is v By Nodal method - Sum of total current Exit from 82 2 40 Burns why Egn In 25 12 a node is zero SA 1 342 fs I, 2 12V • By Nodal method at e point V + V-V2 + V-V3 +3-5=0 circuit t 4 8 2 av, tv-V2 + 40-4V3 = 16 74-V2-4V3 = 16 -(1) By modal method at 2 point V2 + V₂ V3 4 V₂-V, +4V2 +2V2-2V₂ = 0 -V + 7V2-2 V3 =0 - (ii) V₂-V, + 8 2 २. 4 By nodal method at V3 point V₃-12 + V₃-V, + V3-V₂ - 3=0 8 V3-12 + 4V3-40, +2 V3-2V2 =24 -4V, - 2V2 + 7 V3 = 36 -lii) from Eq. (i) V = 16+₂+483 7 substitute u in Eq. (ii) -(16+ V2 +43) +7V2 - 2V3 = 4802-1853 216 V2 = 16+ 18V3 48 substitute V, and ₂ in Eq. (in -41467 V 1993-2016 +13 413 ) + 7V8 2 36 7

+7V3=36 -50" 48 6 + 16+ - 2 16+ 1853 48 2.935 V3 = 36 r! V3 = 12-266 substitute V3 value in z Equation V2 = 16+18V3 = 16+18 X 12-266 48 48 Va = 4.933 substitute Iz and a value in Y Equation Viz 16+₂ +4 V3 =1674.933 + 4x12-26 7 7 'vi-104 current in each resistor is shown in circuit to .! I, = N = 10 10 4 -2.5 A Iz = v.-vq 10-4.933 8 .633 A = - g Iz = 4.933 = 2.4 67 A 2 I4 = V2-V3 4.933-12-266 4 -1.833 A 그 4 I 12-26 6-12 = -033 A 8 Is =V3-12 8 I6=,-V3 10-120266 -1.133 A g 2
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