Question

a) al nede vol tses usina node -wroltage Fint techniyve sa SV (ヤ an わ.a 50

Answer 1

The circuit with nodes identified as shown below in the figure.

The circuit with nodes identified as shown below in the figure. Applying Kirchoff's Current Law at node-1 v_1 - 5.5 + v_1 - v_2.2 + v_1 - v_3/100 = 0 20 (v_1 - 5) + (v_1 - v_2) + (v_1 - v_3) = 0 71 v_1 - 50 v_2 - v_3 = 100 -eq.1 Applying Kirchoff's current law at node-2 v_2 - 0/10 + v_2 - v_12 + v_2 - v_3/2 = 0 v_2 + 5 (v_2 - v_1) + 5(v_2 - v_3) = 0 -5 v_1 + 11 v_2 - 5 v_3 = 0 -eq.2 Applying Kirchoff's current law at node-3 v_3 - 5/5 + v_3 - v_2/2 + v_3 - v_1/100 = 0 20 (v_3 - 5) + 50 (v_3 - v_2) + (v_3 - v_1) = 0 -v_1 - 50 v_2 + 71 v_3 = 100 -eq.3 Representing Eq.1, Eq.2, and Eq.3 in the matrix form [71 -5 -1 -50 11 -50 -1 -5 71] [v_1 v_2 v_3] = [100 0 100] [v_1 v_2 v_3] = [71 -5 -1 -50 11 -50 -1 -5 71]^-1 [100 0

Applying Kirchoff's Current Law at node-1

$rac{v_1-5}{5}+rac{v_1-v_2}{2}+rac{v_1-v_3}{100}=0$

.......Eq.1

Applying Kirchoff's current law at node-2

$v_2+5(v_2-v_1)+5(v_2-v_3)=0$

.........Eq.2

Applying Kirchoff's current law at node-3

$20(v_3-5)+50(v_3-v_2)+(v_3-v_1)=0$

.............Eq.3

Representing Eq.1, Eq.2, and Eq.3 in the matrix form

So, the node voltages are