Problem 4-6



Part a)

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:

KCL at node A:

First, determine V2a so that we can get an expression for the current into node A through the 2 W resistor.

VB - VA = - 110 + V2a

V2a = VB - VA + 110

Now write KCL into node A

Simplify and collect terms.

8 VB - 8 VA + 880 + 2 VC - 2 VA - VA = 0

- 11 VA + 8 VB + 2 VC = - 880 (Eq. A)

KCL at node B:

The current into node B through the upper 110 V source is simply the negative of the current through the 2 W resistor found above, so I'll skip the gory details. The current into node B through the lower 110 V source requires that we find V2b, however.

- VB = V2a - 110

V2a = 110 - VB

Now KCL into node B

Simplify and collect terms

3 VA - 3 VB - 330 + 330 - 3 VB + 2 VC - 2 VB = 0

3 VA - 8 VB + 2 VC = 0 (Eq. B)

KCL at node C:

Simplify and collect terms.

3 VA - 3 VC + 8 VB - 8 VC - VC = 0

3 VA + 8 VB - 12 VC = 0 (Eq. C)

Solving Equations A, B, and C yields:

VA = 157.1 V

VB = 82.5 V

VC = 94.29 V


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