Why Is There a Plus Sign in the Terminal Potential Difference Formula?

[lha08]

Homework Statement

I have a question, in one of my problems in the book(too complicated to post here), they ask for the terminal potential difference across a battery. But usually the formula is (Terminal Potential difference)= (emf)-(I X r) where r is the internal resistance. Like in one case, current is flowing from the positive terminal to the negative one and then through the resistor, but then apparently we have to use this formula to calculate the terminal potential difference: (emf) + (I X r)...why is there a plus sign? I'm just wondering can the emf ever be negative or is it only considered as a positive constant? Like when we measure terminal potential difference, do we usually start at the internal resistance and move to the negative to the negative terminal?

Homework Equations

The Attempt at a Solution

 

[xcvxcvvc]

There are voltage drops across resistors when current flows through them. The voltage at the terminal where current enters is more positive than the voltage at the terminal where the current leaves. So if you have current coming in at the direction opposite to what the battery wants, the voltage drop is in the opposite direction too. Therefore, you'd add it instead of subtract it.

You could also use the other equation with the subtraction except for you'd have a negative current, causing the term to be added.