Find V_{fb} and V_{ec} in the circuit.
Image from: Irwin, J. David., and R. M. Nelms. Basic Engineering Circuit Analysis, Tenth Edition. N.p.: John Wiley & Sons, 2010.
Solution:
To figure out V_{fb}, we will write Kirchhoff’s voltage law around the fbcdef loop (Forgot Kirchhoff’s voltage law?). One way to think of this is to imagine a wire connecting node f to node b, and thinking of that as the new loop.
V_{fb}+1V+3V+3V+1V=0
V_{fb}=-8V
To figure out Vec, we will write Kirchoff’s voltage law around the loop ecde.
V_{ec}+3V+3V=0
V_{ec}=-6V
This question can be found in Basic Engineering Circuit Analysis, 10th edition, chapter 2, question 2.25.