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Q.

Two unknown resistances x and y are connected in the left and right gaps of a metre bridge and the balancing point is obtained at 60 cm from the left. When a 20 $Ω$ resistance is connected in parallel to x, the balance point is 50 cm. Calculate x and y (in ohm)

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a

10,20/3

b

20, 30

c

10/3, 20

d

10, 20

answer is A.

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Detailed Solution

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$\frac{x}{y} = \frac{60}{40} = \frac{3}{2}; y = \frac{2 x}{3} \to (1)$
$\begin{array}{l} \frac{(\frac{20 x}{x + 20})}{y} = 1; \frac{20 x}{x + 20} = y \to (2); \frac{20 x}{x + 20} = \frac{2 x}{3} \\ 20 + x = 10 \Rightarrow x = 10 Ω; y = \frac{2 x}{3} = \frac{20}{3} Ω \end{array}$

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Two unknown resistances x and y are connected in the left and right gaps of a metre bridge and the balancing point is obtained at 60 cm from the left. When a 20Ω resistance is connected in parallel to x, the balance point is 50 cm. Calculate x and y (in ohm)