Write a complete set
of nodal equations which, if solved, would yield values for all
of the node voltages. USE THE NODE VOLTAGES SHOWN. You DO NOT
have to simplify or solve the equations, just write them down.
However, the ONLY variables in your final set of equations should
be the node voltage variables.
V1 = VD - VC
I2 = (VB - VA) / 6K
Express the values of all voltage sources directly connecting two essential nodes in terms of the node voltages.
VA = 9 V1
Substituting for V1 gives
VA = 9 (VD - VC)
VC - VB = 15
Now form supernodes using these voltage sources.
Node A is in a supernode with the reference node, so no KCL equation required.
Node D: I will sum the currents INTO node D
First, determine V8 in order to get the current through the 8K resistor.
VB - VD = - 5 + V8
V8 = VB - VD + 5
KCL into node D:
V8 / 8K + (VC - VD) / 1K + 3m = 0
(VB - VD + 5) / 8K + (VC - VD) / 1K + 3m = 0
KCL out of supernode B/C:
(VB - VA) / 6K + V8 / 8K + (VC - VD) / 1K + VC / 18K - 6 I2 = 0
(VB - VA) / 6K + (VB - VD + 5) / 8K + (VC - VD) / 1K + VC / 18K - 6 (VB - VA) / 6K = 0