Problem 4-10


Find Vo


I will choose node d as the reference node and assign node voltages VA, VB, and VC to nodes a, b, and c respectively. Thus the equations are:

Node A forms a supernode with the reference node due to the 75 V source (shown with a dotted outline):

VA = 75

KCL at node B:

Simplify and collect terms

10 VA - 10 VB + 5 VC - 5 VB - 4 VB = 0

10 (75) - 19 VB + 5 VC = 0

- 19 VB + 5 VC = - 750 (Eq. B)

KCL at node C:

Simplify and collect terms.

4800 + VA - VC + 20 VB - 20 VC - 4 VC = 0

4800 + 75 + 20 VB - 25VC = 0

20 VB - 25VC = - 4875 (Eq. C)

Solving Equations B and C yields:

VA = 75 V

VB = 115 V

VC = 287 V

Thus since Vo = VB - VA

Vo = 115 - 75
Vo = 40 Volts


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