Given below find the current in the wire BD.

Explanation

Let us asing B as reference node and take its potential
=0. As nodes B and D are directly connected with
a conducting wire, hecne potential of node D will
also be zero. Then write the potential of other nodes,
Corresponding currents are shown in node, D
`I_1 = I_2 = I_3`
or `I_3= 5 -4 =1A`
Therefore, current in wire BD in 1A, form D to B

ii. Let us assume the potential of point D to be zero.
the potentials at different points can be assigned as
shown in Fig. 5.11.6. From circuit diagram, it is clear
that current in `2Omega` resistance will be zero as potential
difference across it will be zero. Hecne `I_1 = 0.`

The current through `5Omega` resistance is `I_2 = 4A.` Hence,
at junction `B, I_2 + I_1 + I_3, As I_1 = 0, so I_3 = I_2 = 4A.`
Hence current in wire BD will be 4A.
iii. Let us assume the potential of point B and D be 0V and xV, respectively. Then the potential at different
points can be assigned as shown in Fig. 5.117.

At niode D,
`I_1 +I_2 +I_3 = 0`
`((x + 20))/(5) + ((x-10))/(2) +((x-10))/(2) = 0 or x =5 V`
`I_3 = ((x -10)/(2)) = (5-10)/(2) = -(5)/(2)A`
or 5/2 current will flow from B to D.