Use Kirchhoff ’s rules to determine the potential difference between the points A and . . .

Question : Use Kirchhoff ’s rules to determine the potential difference between the points A and D. When no current flows in the arm BE of the electric network shown in the figure.

Doubt by Manasvini

Solution : 

Applying Junction Rule at the Junction E
I₁=I₂+I₃ — (1)

Applying loop rule in loop 1
2I₁+3I₁+R₁I₃=6+1+3
5I₁+R₁I₃=10
But current through BE is zero i.e I₃=0
5I₁+R(0) = 10
5I₁+0 = 10
5I₁=10
I₁=10/5
I₁ = 2 A — (2)

Applying loop rule in loop 2

RI₂-R₁I₃ = 4-3
RI₂-R₁I₃=1
But current through BE is zero i.e I₃=0
RI₂-R(0)=1

RI₂=1

Putting I₃=0 in eq (1) then I₁=I₂
RI₁=1
R(2)=1 [Using eq (2)]

R = 1/2
R = 0.5 Ω

Now Calculation of Potential between A and D using the Path ABCD

= 6+4-RI₂
= 10-0.5(2)

= 10-1

= 9 V

Alternate : Now Calculation of Potential between A and D using the path AFED

=-2I₁+1-3I₁

=-5I₁+1

=-5(2)+1

=-10+1

=-9 V
=|-9| V

= 9 V