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Current Electricity

Question
CBSEENPH12039554

A rectangular loop has a sliding connector PQ of length

  • straight I subscript 1 space equals space straight I subscript 2 space space equals space fraction numerator straight B space calligraphic l straight v over denominator 6 straight R end fraction comma space fraction numerator straight B space calligraphic l straight v over denominator 3 straight R end fraction
  • straight I subscript 1 space equals space minus straight I subscript 2 space equals space fraction numerator straight B space calligraphic l straight v over denominator straight R end fraction comma space straight I space equals fraction numerator 2 straight B space calligraphic l straight v over denominator 3 straight R end fraction
  • straight I subscript 1 space equals space straight I subscript 2 space space equals space fraction numerator straight B space calligraphic l straight v over denominator 3 straight R end fraction comma space straight I space equals space fraction numerator 2 straight B space calligraphic l straight v over denominator 3 straight R end fraction
  • straight I subscript 1 space equals straight I subscript 2 space equals space straight I space equals space fraction numerator straight B space calligraphic l straight v over denominator straight R end fraction

Solution

C.

straight I subscript 1 space equals space straight I subscript 2 space space equals space fraction numerator straight B space calligraphic l straight v over denominator 3 straight R end fraction comma space straight I space equals space fraction numerator 2 straight B space calligraphic l straight v over denominator 3 straight R end fraction

A moving conductor is equivalent to a battery of emf
= vBI
Equivalent circuit I = I1 + I2

Applying Kirchhoff's law
I1R + IR -vBl = 0 .... (i)
I2R + IR -vBl = 0 .... (ii)
Adding Eqs. (i) and (ii), we get
2IR + IR = 2vBI
I = 2VBI/3R
I1 = I2 = VBI/3R

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