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A cell develops the same power across tw...

A cell develops the same power across two resistances `R_(1)` and `R_(2)` separately. The internal resistance of the cell is

Text Solution

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Let r be the internal resistance of the cell and E its EMF.
When connected across the resistance `R_(1)` in the circuit, current passing through the resistance is
`i=E/(R_(1)+r)`, `therefore P_(1) =i^(2)R_(1) =(E/(R_(1)+r))^(2)R_(1)`
Similarly `P_(2) =((E)/(R_(2)+r))^(2)R_(2)`, Given that `P_(1) =P_(2)`
Substituting the values, we get, `r = sqrt(R_(1)R_(2))`
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