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With standard resistances 2.0Ω and 1.0Ω in the gaps of a metre bridge, the balancing length is 66.9 cm from the higher resistance A of the bridge wire. When the resistances are interchanged, the balancing length is 33.5 cm from the same end A. With an unknown resistance X and standard 1.0Ω in the gaps, the balancing length is 59.7 cm from the end A nearer to X. Then value of X is

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a

0.675 Ω

b

0.670 Ω

c

0.680 Ω

d

1.481 Ω

answer is B.

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Detailed Solution

21=66.9+α33.1+β and 12=33.5+α66.5+βsolving we get, α=−0.1cm and β=0.3cmX1=40.3−0.159.7+0.3=40.260.0=0.67

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With standard resistances 2.0Ω and 1.0Ω in the gaps of a metre bridge, the balancing length is 66.9 cm from the higher resistance A of the bridge wire. When the resistances are interchanged, the balancing length is 33.5 cm from the same end A. With an unknown resistance X and standard 1.0Ω in the gaps, the balancing length is 59.7 cm from the end A nearer to X. Then value of X is