Introductory circuits problem

[Miike012]

My question is why did they choose to calculate the voltage across a circuit element as vi - vf because it seems contradictory.
More detail is in the document.

Someone please answer because this has been bothering me.
THank you.

 

[Miike012]

My guess is that instead of calculating the potential energy drops/gains of current they are calculating the potential energy drops/gains of the circuit elements which is the negative of the potential energy drops/gains of current. It's just frustrating because the book doesn't explain why they are doing what they are doing. Are there any first semester circuits books that give explanations? The book I am reading from is
https://www.amazon.com/dp/0470633220/?tag=pfamazon01-20

 

[meBigGuy]

If you use Vi-Vf then you would change the signs. Vi -Vf = -(Vf-Vi). When you calculated it you used Vf-Vi.

BTW, Vr1 + Vr2 - M = 0.

When you start at the bottom, you first go into the - side of the battery, and then into the + side of two resistors.

Read the wikipedia page on kirchoffs voltage law.