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

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)

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  • 1 month ago

    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

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