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Question 12

The value of unknown resistance $$(x)$$ for which the potential difference between $$B$$ and $$D$$ will be zero in the arrangement shown, is :

Solution

given that potential difference between B and D is zero, the bridge is balanced

so we use:

left top / left bottom = right top / right bottom

left top:
24 ∥ (12 + 12) = 24 ∥ 24 = 12

left bottom:
12 ∥ 12 = 6, then in series with x → 6 + x

right top:
1 ∥ 1 = 0.5

right bottom:
0.5

so,

12 / (6 + x) = 0.5 / 0.5 = 1

12 = 6 + x

x = 6 Ω

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