Develop a set of equations using nodal analysis and solve fo

Develop a set of equations using nodal analysis and solve for the node voltages v_1, v-2, and v_3 in Figure 1, R_1 = 4 ohm, R_2 = 2 ohm, R_3 = 10 ohm, R_4 = 20 ohm, R_5 = 5 ohm, and i_s = 200 mA.

Solution

apply nodal analysis at node v1.

(v1/4)+(v1-v2)/2+0.2=0

v1[(1/2)+(1/4)]+v2(-1/2)=-0.2 ------------------(1)

apply nodal analysis at node v2.

(v2-v1)/2+(v2/10)+(v2-v3)/20=0

v1(-1/2)+v2[(1/2)+(1/10)+(1/20)]+v3(-1/20)=0 ------------------(2)

apply nodal analysis at node v3.

(v3/5)+(v3-v2)/20=0.2

v2(-1/20)+v3[(1/5)+(1/20)]=0.2 --------------------(3)

from equations (1),(2) and (3)

v1=-0.469 volts.

v2=-0.30434 volts.

v3=0.73913 volts.