A potentiometer wire is $$100cm$$ long and a constant potential difference is maintained across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at $$50cm$$ and $$10cmfrom$$ the positive end of the wire in the two cases. The ratio of emf’s is

Question

A potentiometer wire is $$100cm$$ long and a constant potential difference is maintained across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at $$50cm$$ and $$10cmfrom$$ the positive end of the wire in the two cases. The ratio of emf’s is

Infinity Learn · Accepted Answer

Suppose two cells have emfs∈$$1$$ and ∈$$2$$. also ∈$$1$$>∈$$2Potential$$ difference per unit length of the potentiometer $$wire=k$$ When ε$$1$$ and ε$$2$$ are in series and support each other then ε$$1+$$ε$$2=50$$×κ……..(1) When ε$$1$$ and ε$$2$$ are in opposite direction ε$$1-$$ε$$2=10$$×k……..(2) On adding eqn. (1) and eqn. (2) $$2$$ε$$1=60k$$⇒ε$$1=30k$$ and ε$$2=50k-30k=20k$$∴  ε$$1$$ε$$2=30k20k=32$$

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