Determine the node voltages
in the following circuit.
NOTE: V2 was not on the original
diagram, but was added to help solve the problem.
There are no voltage sources, nor are there any dependent sources, so all we need to do is write a KCL equation at each of the essential nodes other than the reference node.
Node A:
Summing the currents INTO node A gives
1m - VA / 4K + (VB - VA) / 8K = 0
Collecting terms and simplifying gives
3 VA - VB = 8 (Equation 1)
Node B:
Summing the currents into node B gives
(VA - VB) / 8K - VB / 16K - 2m = 0
Collecting terms and simplifying gives
2 VA - 3 VB = 32 (Equation 2)
Solving Equation 1 and Equation 2 yields
VA = - 1.143
VB = - 11.43