Find Vae and Vef in the circuit

Find V_{ae} and V_{ef} 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 find V_{ae}, we will write Kirchhoff’s voltage law around the loop aefa (Forgot Kirchhoff’s voltage law?). One way to think of this is to imagine a wire connecting nodes a to e and thinking of that as a loop.

V_{ae}+12V-6V=0

V_{ae}=-6V

To find Vef, we will write Kirchhoff’s voltage law around the loop cfedc.

V_{cf}+5V+6V-12V=0

V_{cf}=1V

This question can be found in Basic Engineering Circuit Analysis, 10th edition, chapter 2, question 2.26.