Find the potential difference between points B and D in the figure below.

Explanation

Here since all the resistance are of same value, you need not calculate the value of current . Just redraw the circuit as follows , showing the direction of current flow and relative higher and lower potential termial.

Both the upper and lower branch of resistances are in parallel with 2V, so both will have same total potential of 2V, Also since each brach has three equal resistors of ` 5Omega` the `2V` potential will equally divide among the three because all three are in serires. The potenital difference across each resistance has been shown below.

Now start moving from point B to D through point A.
`V_(B) + (2)/(3) + (2)/(3) - (2)/(3) = V_(D)`
` therefore V_(B) - V_(D) = (2)/(3) V `