Problem 4-29

Use the node-voltage method to determine the power developed by the 60 volt source. Note that the node labels (in Blue) were not on the original diagram, but are part of step 1: label all essential nodes.

Define the dependent source parameters in terms of the node voltages.

v_D = V_C - V_B

i_f = - V_C / 200

Both voltage sources directly connect two essential nodes, so express their values in terms of the node voltages and form supernodes.

Independent source:

V_B = 60 (Equation 1)

Dependent source

175 i_f = V_D - V_A

Substitute for i_f.

175 (- V_C / 200) = V_D - V_A

Multiply by 200 and collect terms.

- 175 V_C = 200 V_D - 200 V_A
200 V_A - 175 V_C - 200 V_D = 0 (Equation 2)

Node C is the only remaining single essential node.
Nodes A and C form a supernode.
Node B is in a supernode with the reference node, so no KCL needed there.

Write KCL at node C and supernode A/D.

Node C:

Multiply through by 200

Insert Equation 1 and collect terms

(Equation 3)

Supernode A/D

Multiply through by 400

Insert Equation 1

Collect terms

(Equation 4)

Solving Equations 2, 3,m and 4 yields

V_A = - 60.75
V_C = 30
V_D = - 87

Finally, to find the power developed by the 60 volt source, we need the current through it (up). This is equal to the current out of node B through the 10 ohm and 5 ohm resistors.

i₆₀ = (60 + 60.75) / 10 + (60 - 30) / 5
i₆₀ = 18.075 A

So the power developed by the 60 volt source is

P = VI = 60 (18.075)
P = 1084.5 W

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