When does the potential difference between the two terminals of the battery be zero?

I think it will be zero if the battery is consumed entirely or when the circuit is open.
I thought a lot but have no good answer, please help

Agree if the battery is dead BUT

If the circuit is open the voltage is whatever the battery was charged to.
If the circuit is "shot circuited", the terminals connected by a thick wire of zero resistance, the current becomes infinite and the voltage zero
V = i R
V = i (0) = 0

Ok, but is there a wire with no resistance.

And why we neglict the internal resistance of the battery (r)?

To determine when the potential difference between the two terminals of a battery is zero, we need to consider two scenarios:

1. Battery Consumed Entirely: When a battery is fully consumed, it means that it has reached its maximum discharge, and it can no longer supply any electric potential difference. In this case, the potential difference between the two terminals of the battery will be zero.

2. Open Circuit: When a battery is connected to a circuit, it creates a closed loop for the flow of electric current. However, if the circuit is open, meaning there is a gap or break in the path of the circuit, no current can flow. In this scenario, since there is no current flowing, the potential difference between the two terminals of the battery will remain zero.

So, you are correct in your understanding that the potential difference between the two terminals of a battery will be zero when the battery is consumed entirely or when the circuit is open.