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 difference between A and D.

Explanation

As per question no current flows through 4 `Omega` resistance. Hence current in branch EB is zero and current flowing through branch EDCB is I.
` therefore ` For mesh AFEBA, we have
- 1.I - 1.I - 6 + 9 = 0 ` rarr I = 1.5 A`
Now for mesh BEDCB, we have
`6 - R xx 1.5 - 3 = 0 rArr R = 2Omega`
Moreover, potential difference `V_A - V_D =9- 3 -IR = 9 - 3- (1.5) xx (2) = 3 V`