Determine the value of R in the circuit shown in
figure, when the current is zero in the branch CD.

Explanation

The current in the branch CD is zero, if the
potential difference across CD is zero.
That means, voltage at point C = voltage at point D.
Since no current is flowing, the branch CD is
open circuited. So the same voltage is applied
across ACB and ADB
`V_10=Vxx10/15rArrV_R=VxxR/(20+R)`
`:.` `V_10=V_r` and` Vxx10/15=VxxR/(20+R)`
`R=40Omega` Ans.