Question

Can the potential difference across a battery be greater than its emf?

Answer 1

If the electric potential difference between two locations is 1 volt, then one Coulomb of charge will gain 1 joule of potential energy when moved between those two locations. Because electric potential difference is expressed in units of volts, it is sometimes referred to as the voltage.

Complete step-by-step answer:
In 1st case :The battery is discharging.
let us assume that the battery is discharging,
So the emf of the battery is E, and the potential difference is V
Assume that the internal resistance is r
According to the case the battery is discharging,
So, the potential difference across the battery is,
$V = E - ir$
Here we can say the potential difference is surely less than emf
In the 2nd case:The battery is charging.
The current flow through the lower end to higher end
So we can say the potential difference is,
$V = E + ir$

Here we can see the potential difference is greater than emf.

So, the answer is when the battery is charging the potential difference can be greater than emf.

Note: The voltage or electric potential difference across the terminals of a cell when no current is drawn from it. The electromotive force (emf) is the sum of the electric potential differences produced by a separation of charges (electrons or ions) that can occur at each phase boundary (or interface) in the cell.