Consider the circuit shown in the figure. Suppose that vs = 50 V.?

Question

a) Use the node voltage method to find Vo. (3 significant figures)

b) Find the magnitude of the total power supplied in the circuit. (3 significant figures)

Answer 1

KCL at VΔ

(VΔ-50)/500+ VΔ/1000+( VΔ-Vo)/2000 = 0 Multiply equation by 2000

4VΔ-200+2VΔ+VΔ-Vo = 0 -----> Vo = 7VΔ - 200

KCL at Vo

(Vo-VΔ)/2000 + 10Vo/2000 - VΔ/750 = 0  Multiply equation by 2000

11Vo - VΔ - 8VΔ/3 = 0

Vo = VΔ/3

But Vo = 7VΔ - 200 So VΔ/3 = 7VΔ - 200 Multiply equation by 3

600 = 20VΔ so VΔ = 600/20 = 30V and Vo = VΔ/3 = 10V

Vo = 10V a) <<<<<

b) Vs delivers 50V * 40mA = 2W

The current source delivers 10*30/750 = 0.4W so 2.4W are delivered. b)

Consumed by resistance:

V1 = VΔ = 30, Vo = V2 = 10

20²/500 + 30²/1000 + 20²/2000 + 10²/200 = 2.4W Checks