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.