Determine the value of R in the circuit shown in figure, when the currnet in zero in the brance CD.

Explanation

The current in the branch CD is zero, if the potential difference across CD is zero.
That means, voltaege at point C = voltage at point D.
Since no current in flowing, the brance CD is open circuited. So the same voltage is applied across ACB and ADB.
Since no current is flowing, the brance CD is open circuited. So the same voltage is applied across ACB and ADB
`V_(10)=Vxx10/15rArrV_(R)=VxxR/(20xxR)`
`thereforeV_(10)=V_(R)" and "Vxx10/15xxR/(20xxR)`
`thereforeR=40 Omega`