Question

R 0 Rz 3 + VA R3 + 3 VA Vg + Ig mm HU WW Ry you are given: Ri = R2 = Rs = RA 19, V, = 8V and 1, - 8A. a) Draw the graph and identify a tree that satisfies the guidelines (include resistor RA in the tree as well). b) Formulate and solve the node voltage equations in matrix form (stick to the given node numbering!). c) Compute all the powers, and verify that the total power delivered equals the total power absorbed.

Answer 1

TU U I 4- nodes. 6-branches IVA 책 ܩܽܘ Ig = For Chear oriented graph. R4 voltage source short current source open. Chear siented graph 2 TT TU tree I is connected sub graph, which contains all the nodes without any vo closed loop. I UT n + 5-branches 성 3 3-nodes 4 Tu T(1,2,3,4) (ar) TCI,2,3)

VA Ri=IRUR nodal analysis R2 =12 V + + here un ug = 8 10 148 PA Nin >3VA, lat node uz 88 kelapply at ve .-8 tuaru VQ-8 in 14 2UgUz = 16. - kad apply at node u * Uzun U + Ug+IVA here VA = U2-8 20 302 -V2+2UA- 30-U2+3(12-8)=0 202 +70g = 24 - 2 1 Un 24 2 Fram tuese {quasion = U2 = 9: U = 2. *4=1 hore power at here I2 - I = vi-U2 874-7. ug Qos power at ng = (ug)(91) = (5)(-1) = -f cits. Cite absolbrug, . Current entous't' power at Ri= (11) CU = I watts leauging -) Ig =) (Ig)CO2) =(8)(9) = 72 ucalts U.2- U = 7A power at R2 =) (12)2 x R = 49 watts power at Ry =) ( ²x here I4 = Ug+30A 3 +30 = 2+3 (N2-V) = 2+3(1) = 5 pour at Rq (14)'x125 watts 344= 14)(JUA) = 503)(1) 15 watts = power delelerrig PRI + PR2 - PR2 + PR4+ Pug Pig + P3uA 87 watts 4 watts power at power absorbing 87 watts