Use nodal analysis to find V0 given that Vs 5V Is 9A R1 7

Use nodal analysis to find V_0 given that V_s = 5V, I_s = 9A, R_1 = 7 Ohm, R_2 = 10 Ohm, R_3 = 2 Ohm, R_4 = 6 Ohm, and R_5 = 9 Ohm. The best choice for the reference node is the bottom node, since that node has the most elements connected to it and it has one terminal of the voltage source connected to it. Use the convention from Hayt, Kemmerly and Durbin that currents enter the node from current sources and leave the node through resistors. The nodal analysis equation at node 1: 1 V_1 + 0 V_2 + 0 V_3 + 0 V_4 = 5 The nodal analysis equation at node 2: -10 V_1 + 32 V_2 + -35 V_3 + 0 V_4 = 0 The nodal analysis equation at node 3: 0 V_1 + -9 V_2 + 14 V_3 + -2 V_4 = 0 The nodal analysis equation at node 4: 0 V_1 + 0 V_2 + -1/9 V_3 + 1/9 V_4 = 9 V_1 = 5 V V_2 = V V_3 = V V_4 = V V_0 = V

Solution

from the circuit v1=5 volts.

apply nodal analysis at node v2.

v2/10+[v2-5]/7+[v2-v3]/10=0

v2[(1/7)+(1/10)+(1/10)]+v3[-1/10]=5/7 -----------(1)

apply nodal analysis at node v3.

v3/6+(v3-v2)/2=9

v2[-1/2]+v3[0.5+(1/6)]=9 -------------(2)

from equations (1) and (2)

v2=7.706 volts

v3=19.28 volts

v4=v3-IS*R4=19.28-9*9*=-61.72 volts.