Find all node voltages in the circuit with respect to the bottom node as ground, where , , , , , . Use both node voltage and loop current methods.

**Solution:**

**Node voltage:**Let the bottom node be ground and other node voltages be (left), (middle) and (right).

Solving this we get:

Alternatively, use the figure on the right and assume between the current and voltage sources is grounded , then , and denote previous ground by . We have

Solving this we get:

This is result is equivalent to the previous one. To see this, we subtract 48.7 from all node voltages so that becomes the ground, and get

We see that the second method is easier.**Loop current:**Let the loop currents be (top), (left) and (right).

Solving this we get:

Alternatively, use the figure on the right and assume loop currents through voltage source , through current source and through . We have

Solving this we get:

Current through is , current through is , same as before.We see that the second method is easier.