In a metre bridge experiment null point is obtained at 20 cm from one end of the wire when resistance X is balanced against another resistance Y. If X < Y, then where will be the new position of the null point from the same end, if one decides to balance a resistance of 4X against Y?

50 cm

80 cm

40 cm

70 cm

Solution

50 cm

We have from meter bridge experiment,
$straight R subscript 1 over straight R subscript 2 space equals space fraction numerator begin display style calligraphic l subscript 1 end style over denominator calligraphic l subscript 2 end fraction comma space where space calligraphic l subscript 2 space equals space left parenthesis 100 space minus space calligraphic l subscript 1 right parenthesis space c m I n space t h e space f i r s t space c a s e comma space X divided by Y space equals space 20 divided by 80 I n space t h e space s e c o n d space c a s e space fraction numerator 4 X over denominator Y end fraction space equals space fraction numerator calligraphic l over denominator 100 minus calligraphic l end fraction calligraphic l space equals space 50 space c m$

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