I'm doing an internal of a battery resistance experiment but not familiar with this formula V = ε- Ir. What is the I in this formula?

Answer 1

the current
if you have internal resistance r
and current i
then the voltage drop due to the internal resistance =i r
so the real battery voltage you see across your outside load is the battery resistance - that loss

Answer 2

I mean the battery VOLTAGE - i r

Answer 3

Is that why the battery warm up afterward ?

Answer 4

Yes

Answer 5

i^2 r is the power wasted on that internal resistance, which is indeed expressed as heat.