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Q.

Consider a metre bridge whose length of wire is 2m. A resistance of 10 $Ω$ is connected across one gap of the meter bridge and an unknown resistance is connected across the other gap. When these resistances are interchanged the balance point shifts by 50 cm. What is the value of the unknown resistance?

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a

10 $Ω$

b

16.7 $Ω$

c

None of the above

d

250 $Ω$

answer is C.

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Detailed Solution

Say, the unknown resistance = X
$Case 1 : 10 / X = L_{1} / (200 - L_{1}) Or, {xL}_{1} = 2000 - 10 L_{1} . . . . (i) Case 2 : X / 10 = (L_{1} + 50) / (150 - L_{1}) Or, {xL}_{1} = 150 X - 10 L_{1} - 500 . . . (ii) Comparing equation (i) and (ii) X = 2500 / 150 = 16 .7 Ω$

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