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

Applying Kirchhoff's second law in closed mesh AFEBA , 9V = I × 1 + I × 1 + 4 × 0 = 0 (current in 4Ω is given zero)
or 3 = 2I
or I = 3/2 = 1.5A
now in closed mesh AFEDCBA , 9V = I(1+1) + IR
or 6 = 1.5 × 2 + 1.5R
or 6 = 3 + 1.5R
or R = 3/1.5 = 2Ω
now from point A to point D , (applying Kirchhoff's law for linear part AFED)
VA − I(1+1) = VD
or VA − VD = 1.5 × 2 = 3V