Using kirchhoff's laws, calculate the potential difference across the 8 ohm resistor.
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Dear Student,
You posted an incomplete question, perfect answer to which is rather impossible. But I will explain here about Kirchhoff's law which you can apply to any electrical circuit to get the answer.
# Solution-
In balanced Wheatstone's bridge, zero current flow through galvanometer. Means while applying Kirchoff's law we can neglet this path.
Look at the figure,
No current flows through galvanometer G if circuit is balanced.
Applying Kirchoff's law to
(1) Mesh ABDA,
-I1R1 + (I-I1)R4 = 0
I1R1 = (I-I1)R4 ….(1)
(2) Mesh BCDB,
-I1R2 + (I-I1)R3 = 0
I1R2 = (I-I1)R3 ….(2)
Dividing (1) by (2),
I1R1 / I1R2 = (I-I1)R4 / (I-I1)R3
R1/R2 = R4/R3
This is balancing condition for Wheatstone's bridge.
Best luck for exams buddy...
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