A galvanic cell behaves as electrolytic cell when?

The correct option is Eext > Ecell (which corresponds to $E_{\text{ext}}>E_{\text{cell}}$).

To understand why this happens, let us look at the behavior of a galvanic cell when an opposing external potential ($E_{\text{ext}}$) is applied across it:

1. When $E_{\text{ext}}<E_{\text{cell}}$:
The cell continues to behave as a galvanic cell. Chemical energy is converted into electrical energy, and electrons flow from the anode to the cathode in the external circuit.

2. When $E_{\text{ext}}=E_{\text{cell}}$:
The external potential completely balances the cell potential. As a result, no current flows through the circuit, and no chemical reaction occurs.

3. When $E_{\text{ext}}>E_{\text{cell}}$:
When the opposing external potential exceeds the cell potential, the direction of current is reversed. The electrical energy supplied from the external source now drives a non-spontaneous chemical reaction in the opposite direction. Consequently, the cell behaves as an electrolytic cell, where electrical energy is consumed to drive chemical changes.