Frame and solve the node equations of the network of Fig. Hence, find

1.	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» 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

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»

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

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