Use Kirchhoff's rules to determine the potential difference between the points $A$ and $D$ when no current flows in the arm $BE$ of the electric network shown in the figure

$\text{Step 1: Current in the circuit [Refer Fig.]}$ 

There is no current in $BE$ branch, so the potential difference across resistance $R_1$ will be zero.

$\text{Step 2: Potential difference}(V_A-V_D)$ 

To find Potential difference between Points A and D, we can see a path ABED, such that, the branches AB and ED have batteries only and there is no current in branch EB.

Therefore, we can directly find the required potential difference without finding the current in all the branches.

So, In path $ABED$ 

                 $V_A-6-3-0=V_D$ 

                  $\boxed{V_A-V_D=9V}$

$\text{Note:}$ There is no need to apply KVL to find current in all the branches.