Example 4: (Homework) Find all node voltages with respect to the top-left corner treated as reference node:

, , , , , .

Solution: For convenience, we first assume the bottom node is reference point, and we have node voltages (left), (middle) and (right). Applying KCL to , we get

Solving this equation we get . Now treating as reference point (ground), we subtract from all node voltages to get , , , .

When the middle node is treated as ground, we can still solve the problem the same way as above by treating the bottom node is the ground, and then subtract from each of the voltages to get the answer.

Ruye Wang 2019-02-04