A galvanic cell can be converted to an electrolytic cell when

\(E_{ext} > 1.1\, \ V\)

The correct answer is option 3. \(E_{ext} > 1.1\, \ V\).

A galvanic cell can be converted to an electrolytic cell when an external voltage (potential) is applied to the cell. This external voltage opposes the spontaneous electrochemical reaction that occurs in a galvanic cell. The electrochemical cell operates as a galvanic cell when \(E_{\text{cell}} > 0\) (positive cell potential).

The standard cell potential (\(E^\circ_{\text{cell}}\)) is related to the equilibrium constant (\(K\)) for the cell reaction through the Nernst equation:

\[ E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q \]

where:
\(E_{\text{cell}}\) is the actual cell potential.
\(E^\circ_{\text{cell}}\) is the standard cell potential.
\(R\) is the ideal gas constant.
\(T\) is the temperature in Kelvin.
\(n\) is the number of moles of electrons exchanged in the reaction.
\(F\) is Faraday's constant.
\(Q\) is the reaction quotient.

Now, considering the given options:

1. \(E_{\text{ext}} < 1.1\, \ V\): If the external voltage is less than the standard cell potential, the cell will continue to operate as a galvanic cell.

2. \(E_{\text{ext}} = 1.1\, \ V\): This is the boundary condition where the external voltage matches the standard cell potential. The cell may operate near equilibrium, and it is theoretically possible to convert it to an electrolytic cell.

3. \(E_{\text{ext}} > 1.1\, \ V\):  If the external voltage is greater than the standard cell potential, the cell can be converted to an electrolytic cell.

4. The chemical reaction stops on completion:  This statement is not relevant to the conversion of a galvanic cell to an electrolytic cell. The conversion occurs when an external voltage is applied.

Therefore, the correct answer is 3. \(E_{\text{ext}} > 1.1\, \ V\).