Problem 4-20



I will choose the bottom node as the reference node and assign node voltages VA, VB, and VC to the remaining nodes.

Define vD (used to define the dependent source) in terms of node voltages.

vD = VA - VB

Node A forms a supernode with the reference node due to the 50 V source (shown with a dotted outline):

VA = 50

Nodes B and C also form a supernode due to the dependent voltage source (shown with a dotted outline):

VB - VC = vD / 5 = (VA - VB) / 5

VB - VC = (50 - VB) / 5

1.2 VB - VC = 10 (Eq. 1)

KCL at supernode B-C:

Simplify and collect terms (LCD = 390)

39 VA - 39 VB - 13 VB - 10 VC - 5 VC = 0

39 (50) - 52 VB - 15 VC = 0

- 52 VB - 15 VC = - 1950 (Eq. 2)

 

Solving Equations 1 and 2 yields:

VA = 50 V

VB = 30 V

VC = 26 V = Vo


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