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?

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

I mean the battery VOLTAGE - i r

Is that why the battery warm up afterward ?

Yes

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

In the formula V = ε - Ir, the 'I' represents the electric current flowing through the circuit. This formula is known as Ohm's law, which relates the voltage (V) across a circuit component to the current (I) flowing through it, the resistance (R) of the component, and the electromotive force (ε) provided by the battery.

To determine the value of the current (I), you need to measure the voltage (V) across the circuit and the electromotive force (ε) provided by the battery. Then, you can use the formula rearrangement:

I = (ε - V) / R

Here's a step-by-step guide on how to use Ohm's law to solve for the current (I) in your battery resistance experiment:

1. Measure the voltage across the circuit component using a voltmeter. Let's say you get a reading of V.

2. Measure the electromotive force (voltage) of the battery using a voltmeter. Let's say you get a reading of ε.

3. Measure the resistance (R) of the circuit component using an ohmmeter or by knowing its value from the circuit diagram or component specifications.

4. Substitute the measured values into the formula.

I = (ε - V) / R

5. Calculate the result to find the value of current (I) flowing through the circuit.

Keep in mind that in order to get an accurate reading of the current, the circuit needs to be connected properly and be in a closed loop. Also, double-check the unit of the measured values to ensure they are consistent (e.g., volt, ampere, ohm).