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Two cells of emf E each and internal res...

Two cells of emf E each and internal resistance `r_(1)` and `r_(2)` are connected in series across a load resistance R. If potential difference across the first cell is zero, then find the relation between `R, r_(1)` and `r_(2)`

Text Solution

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Current l from positive electrondes of both are equal .
`l = (E_(eq))/(R+r_(eq)) = (2E)/(R+ (r_(1) + r_(2)))`
Potential difference across first cell = `V_(A) - V_(B) = 0`
` rArr E - Ir_(1) = 0`
`rArr E - (2E)/(R + (r_(1) + r_(2))) r_(1) = 0`
`rArr R + r_(1) + r_(2) - 2r_(1) = 0`
` rArr R + r_(2) - r_(1) = 0`
`rArr r_(1) = R + r_(2) rArr R = (r_(1) - r_(2))`
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