Question

Frame and solve the node equations of the network of Fig. Hence, find the total power consumed by the passive elements of the network.

Answer 1

The node equation for node 1 is

V₁(1 + 1 + 1/0.5) - V₂/0.5 - 15/1 = 0

or 4V₁ - 2V₂ = 15

Similarly, for node 2, we have

V₁(1 + 1/2 + 1/0.5) - V₂/0.5 - 20/1 = 0

or 4V₁ − 7V₂ = − 40 ...(ii) 

∴ V₂ = 11 volt and V₁ = 37/4 volt 

Now,

I₁ = (15 - 37/4)/I = 23/4A = 5.75A; I₂ = (11 - 37/4)/0.5 = 3.5A

I₄ = 5.75 + 3.5 = 9.25A, I₃ = (20 - 11)/1 = 9A; I₅ = 9 - 3.5 = 5.5A

The passive elements of the network are its five resistances. Total power consumed by them is 

= 5.75² × 1 + 3.5² × 0.5 + 9² × 1 + 9.25² × 1 + 5.5² × 2 = 266.25