n identical cells each of EMF E and internal resistance R are joined in series except one cell (A) is joined with reversed polarity. The potential difference across A is
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let assume that current for N identical cells is = i1 = ne/(nr + r). And the current for one opposite cell is =i2 =e/(nr+r). That means the net current in the circuit is = i1 - i2 = e(n-1)/(nr +r). The voltage across the cell = i*nr.
i = e(n-1)/(nr+r)
or, i*nr = {e(n-1)/r(n+1)}*nr
or, v = e(n-1)n/()n+1 [v = voltage across the opposite cell]
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