Using Kirchhoff's rules determine the value of unknown resistance $R$ in the circuit so that no current flows through $4\Omega$ resistance. Also find the potential between $A$ and $D$.

Applying Kirchhoff's second law in closed mesh AFEBA ,

                              $9-6=I\times 1+I\times 1+4\times 0=0$  (current in $4\Omega$ is given zero)

  or                         $3=2I$

  or                          $I=3/2=1.5A$

now in closed mesh AFEDCBA ,

                             $9-3=I(1+1)+IR$

  or                        $6=1.5\times 2+1.5R$

  or                        $6=3+1.5R$

  or                        $R=3/1.5=2\Omega$

now from  point A to point D , (applying Kirchhoff's law for linear part AFED)

                           $V_A-I(1+1)=V_D$

or                        $V_A-V_D=1.5\times 2=3V$